@article {AKMW, AUTHOR = {Abramovich, Dan and Karu, Kalle and Matsuki, Kenji and W{\l}odarczyk, Jaros{\l}aw}, TITLE = {Torification and factorization of birational maps}, JOURNAL = {J. Amer. Math. Soc.}, FJOURNAL = {Journal of the American Mathematical Society}, VOLUME = {15}, YEAR = {2002}, NUMBER = {3}, PAGES = {531--572 (electronic)}, ISSN = {0894-0347}, MRCLASS = {14E05 (14E15 14L24)}, MRNUMBER = {1896232 (2003c:14016)}, MRREVIEWER = {Alexandr V. Pukhlikov}, DOI = {10.1090/S0894-0347-02-00396-X}, URL = {http://dx.doi.org/10.1090/S0894-0347-02-00396-X}, } @article{AddMRL, AUTHOR = {Addington, Nicolas}, TITLE = {On two rationality conjectures for cubic fourfolds}, JOURNAL = {Math. Res. Lett.}, FJOURNAL = {Mathematical Research Letters}, VOLUME = {23}, YEAR = {2016}, NUMBER = {1}, PAGES = {1--13}, ISSN = {1073-2780}, MRCLASS = {14J35 (14E05 14J28)}, MRNUMBER = {3512874}, DOI = {10.4310/MRL.2016.v23.n1.a1}, URL = {http://dx.doi.org/10.4310/MRL.2016.v23.n1.a1}, } @article {AL, AUTHOR = {Addington, Nicolas and Lehn, Manfred}, TITLE = {On the symplectic eightfold associated to a {P}faffian cubic fourfold}, JOURNAL = {J. Reine Angew. Math.}, FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's Journal]}, YEAR = {2015}, ISSN = {0075-4102}, DOI = {10.1515/crelle-2014-0145}, URL = {http://dx.doi.org/10.1515/crelle-2014-0145}, } @incollection {ACTP, AUTHOR = {Auel, Asher and Colliot-Th\'el\`ene, Jean-Louis and Parimala, Raman}, TITLE = {Universal unramified cohomology of cubic fourfolds containing a plane}, BOOKTITLE = {Brauer Groups and Obstruction Problems:\ Moduli Spaces and Arithmetic}, YEAR = {2013}, NOTE = {Proceedings of a workshop at the American Institute of Mathematics}, } @article {AdTh, AUTHOR = {Addington, Nicolas and Thomas, Richard}, TITLE = {Hodge theory and derived categories of cubic fourfolds}, JOURNAL = {Duke Math. J.}, FJOURNAL = {Duke Mathematical Journal}, VOLUME = {163}, YEAR = {2014}, NUMBER = {10}, PAGES = {1885--1927}, ISSN = {0012-7094}, MRCLASS = {14F05 (14J10 14J28 14J35)}, MRNUMBER = {3229044}, MRREVIEWER = {Pawel Sosna}, DOI = {10.1215/00127094-2738639}, URL = {http://dx.doi.org/10.1215/00127094-2738639}, } @article {ABBVA, AUTHOR = {Auel, Asher and Bernardara, Marcello and Bolognesi, Michele and V{\'a}rilly-Alvarado, Anthony}, TITLE = {Cubic fourfolds containing a plane and a quintic del {P}ezzo surface}, JOURNAL = {Algebr. Geom.}, FJOURNAL = {Algebraic Geometry}, VOLUME = {1}, YEAR = {2014}, NUMBER = {2}, PAGES = {181--193}, ISSN = {2214-2584}, MRCLASS = {14J35 (14F05 14J28)}, MRNUMBER = {3238111}, MRREVIEWER = {Alan Matthew Thompson}, DOI = {10.14231/AG-2014-010}, URL = {http://dx.doi.org/10.14231/AG-2014-010}, } @article {ABvB, AUTHOR = {Auel, Asher and B{\"o}hning, Christian and Graf von Bothmer, Hans-Christian}, TITLE = {The transcendental lattice of the sextic {F}ermat surface}, JOURNAL = {Math. Res. Lett.}, FJOURNAL = {Mathematical Research Letters}, VOLUME = {20}, YEAR = {2013}, NUMBER = {6}, PAGES = {1017--1031}, ISSN = {1073-2780}, MRCLASS = {14J25 (14C30)}, MRNUMBER = {3228617}, MRREVIEWER = {Fumio Hazama}, DOI = {10.4310/MRL.2013.v20.n6.a2}, URL = {http://dx.doi.org/10.4310/MRL.2013.v20.n6.a2}, } @article {AK, AUTHOR = {Altman, Allen B. and Kleiman, Steven L.}, TITLE = {Foundations of the theory of {F}ano schemes}, JOURNAL = {Compositio Math.}, FJOURNAL = {Compositio Mathematica}, VOLUME = {34}, YEAR = {1977}, NUMBER = {1}, PAGES = {3--47}, ISSN = {0010-437X}, MRCLASS = {14C05 (14C20 14M15 14N10)}, MRNUMBER = {0569043 (58 \#27967)}, MRREVIEWER = {Joel Roberts}, } @book {Baker, AUTHOR = {Baker, H. F.}, TITLE = {Principles of geometry. {V}olume 6. {I}ntroduction to the theory of algebraic surfaces and higher loci}, SERIES = {Cambridge Library Collection}, NOTE = {Reprint of the 1933 original}, PUBLISHER = {Cambridge University Press, Cambridge}, YEAR = {2010}, PAGES = {ii+x+308}, ISBN = {978-1-108-01782-4}, MRCLASS = {01A75 (14-03)}, MRNUMBER = {2850141}, } @article {BM1, AUTHOR = {Bayer, Arend and Macr{\`{\i}}, Emanuele}, TITLE = {Projectivity and birational geometry of {B}ridgeland moduli spaces}, JOURNAL = {J. Amer. Math. Soc.}, FJOURNAL = {Journal of the American Mathematical Society}, VOLUME = {27}, YEAR = {2014}, NUMBER = {3}, PAGES = {707--752}, ISSN = {0894-0347}, MRCLASS = {14D20 (14E30 14F05 14J28)}, MRNUMBER = {3194493}, MRREVIEWER = {P. E. Newstead}, DOI = {10.1090/S0894-0347-2014-00790-6}, URL = {http://dx.doi.org/10.1090/S0894-0347-2014-00790-6}, } @article {BMT, AUTHOR = {Bayer, Arend and Hassett, Brendan and Tschinkel, Yuri}, TITLE = {Mori cones of holomorphic symplectic varieties of {K}3 type}, JOURNAL = {Ann. Sci. \'Ec. Norm. Sup\'er. (4)}, FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure. Quatri\`eme S\'erie}, VOLUME = {48}, YEAR = {2015}, NUMBER = {4}, PAGES = {941--950}, ISSN = {0012-9593}, MRCLASS = {14Fxx (14Exx)}, MRNUMBER = {3377069}, } @article {BM2, AUTHOR = {Bayer, Arend and Macr{\`{\i}}, Emanuele}, TITLE = {M{MP} for moduli of sheaves on {K}3s via wall-crossing: nef and movable cones, {L}agrangian fibrations}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {198}, YEAR = {2014}, NUMBER = {3}, PAGES = {505--590}, ISSN = {0020-9910}, MRCLASS = {14D20 (14E30 14F05 14J28)}, MRNUMBER = {3279532}, DOI = {10.1007/s00222-014-0501-8}, URL = {http://dx.doi.org/10.1007/s00222-014-0501-8}, } @article {Beau, AUTHOR = {Beauville, Arnaud}, TITLE = {Vari\'et\'es {K}\"ahleriennes dont la premi\`ere classe de {C}hern est nulle}, JOURNAL = {J. Differential Geom.}, FJOURNAL = {Journal of Differential Geometry}, VOLUME = {18}, YEAR = {1983}, NUMBER = {4}, PAGES = {755--782 (1984)}, ISSN = {0022-040X}, CODEN = {JDGEAS}, MRCLASS = {32J25 (14J15 32C10 32G13 53C55)}, MRNUMBER = {730926 (86c:32030)}, MRREVIEWER = {N. J. Hitchin}, URL = {http://projecteuclid.org/euclid.jdg/1214438181}, } @article {BeauDet, AUTHOR = {Beauville, Arnaud}, TITLE = {Determinantal hypersurfaces}, NOTE = {Dedicated to William Fulton on the occasion of his 60th birthday}, JOURNAL = {Michigan Math. J.}, FJOURNAL = {The Michigan Mathematical Journal}, VOLUME = {48}, YEAR = {2000}, PAGES = {39--64}, ISSN = {0026-2285}, MRCLASS = {14M12 (14J70)}, MRNUMBER = {1786479 (2002b:14060)}, MRREVIEWER = {Laurent Manivel}, DOI = {10.1307/mmj/1030132707}, URL = {http://dx.doi.org/10.1307/mmj/1030132707}, } @article {BD, AUTHOR = {Beauville, Arnaud and Donagi, Ron}, TITLE = {La vari\'et\'e des droites d'une hypersurface cubique de dimension {$4$}}, JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.}, FJOURNAL = {Comptes Rendus des S\'eances de l'Acad\'emie des Sciences. S\'erie I. Math\'ematique}, VOLUME = {301}, YEAR = {1985}, NUMBER = {14}, PAGES = {703--706}, ISSN = {0249-6291}, CODEN = {CASMEI}, MRCLASS = {14J35 (14C30)}, MRNUMBER = {818549 (87c:14047)}, MRREVIEWER = {Fabio Bardelli}, } @misc {BRS, AUTHOR = {Michele Bolognesi and Francesco Russo and Giovanni Staglian\`o}, TITLE = {Some loci of rational cubic fourfolds}, NOTE = {arXiv:1504.05863}, YEAR = {2015}, } @misc {Bor, AUTHOR = {Borisov, Lev}, TITLE = {Class of the affine line is a zero divisor in the {G}rothendieck ring }, NOTE = {arXiv:1412.6194}, YEAR = {2014}, } @article {BrHB, AUTHOR = {Browning, T. D. and Heath-Brown, D. R.}, TITLE = {The density of rational points on non-singular hypersurfaces. {II}}, NOTE = {With an appendix by J. M. Starr}, JOURNAL = {Proc. London Math. Soc. (3)}, FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, VOLUME = {93}, YEAR = {2006}, NUMBER = {2}, PAGES = {273--303}, ISSN = {0024-6115}, CODEN = {PLMTAL}, MRCLASS = {11D45 (11G35 14G05)}, MRNUMBER = {2251154 (2007h:11042)}, MRREVIEWER = {Clayton Petsche}, DOI = {10.1112/S0024611506015784}, URL = {http://dx.doi.org/10.1112/S0024611506015784}, } @article {CG, AUTHOR = {Clemens, C. Herbert and Griffiths, Phillip A.}, TITLE = {The intermediate {J}acobian of the cubic threefold}, JOURNAL = {Ann. of Math. (2)}, FJOURNAL = {Annals of Mathematics. Second Series}, VOLUME = {95}, YEAR = {1972}, PAGES = {281--356}, ISSN = {0003-486X}, MRCLASS = {14J10 (14G13 14J05 14K20 14M20 14N99)}, MRNUMBER = {0302652 (46 \#1796)}, MRREVIEWER = {H. Popp}, } @article {CTRC, AUTHOR = {Colliot-Th{\'e}l{\`e}ne, Jean-Louis}, TITLE = {Un th\'eor\`eme de finitude pour le groupe de {C}how des z\'ero-cycles d'un groupe alg\'ebrique lin\'eaire sur un corps {$p$}-adique}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {159}, YEAR = {2005}, NUMBER = {3}, PAGES = {589--606}, ISSN = {0020-9910}, CODEN = {INVMBH}, MRCLASS = {14C15 (14G20 20G25)}, MRNUMBER = {2125734 (2005m:14009)}, MRREVIEWER = {Cristian D. Gonz{\'a}lez-Avil{\'e}s}, DOI = {10.1007/s00222-004-0393-0}, URL = {http://dx.doi.org/10.1007/s00222-004-0393-0}, } @article {CrKa, AUTHOR = {Crauder, Bruce and Katz, Sheldon}, TITLE = {Cremona transformations with smooth irreducible fundamental locus}, JOURNAL = {Amer. J. Math.}, FJOURNAL = {American Journal of Mathematics}, VOLUME = {111}, YEAR = {1989}, NUMBER = {2}, PAGES = {289--307}, ISSN = {0002-9327}, CODEN = {AJMAAN}, MRCLASS = {14E05 (14E07 14J25)}, MRNUMBER = {987759}, MRREVIEWER = {Marino Palleschi}, DOI = {10.2307/2374511}, URL = {http://dx.doi.org/10.2307/2374511}, } @incollection {DolCr, AUTHOR = {Dolgachev, Igor V.}, TITLE = {Luigi {C}remona and cubic surfaces}, BOOKTITLE = {Luigi {C}remona (1830--1903) ({I}talian)}, SERIES = {Incontr. Studio}, VOLUME = {36}, PAGES = {55--70}, PUBLISHER = {Istituto Lombardo di Scienze e Lettere, Milan}, YEAR = {2005}, MRCLASS = {14-03 (01A55 01A70)}, MRNUMBER = {2305952 (2008a:14002)}, MRREVIEWER = {J{\'e}r{\'e}my Blanc}, } @article {Edge, AUTHOR = {Edge, W. L.}, TITLE = {The number of apparent double points of certain loci}, JOURNAL = {Math. Proc. Cambridge Philos. Soc.}, FJOURNAL = {Mathematical Proceedings of the Cambridge Philosophical Society}, VOLUME = {28}, PAGES = {285--299}, DOI = {10.1017/S0305004100010148}, YEAR = {1932}, } @article {Fano, AUTHOR = {Fano, Gino}, TITLE = {Sulle forme cubiche dello spazio a cinque dimensioni contenenti rigate razionali del {$4^\circ$} ordine}, JOURNAL = {Comment. Math. Helv.}, FJOURNAL = {Commentarii Mathematici Helvetici}, VOLUME = {15}, YEAR = {1943}, PAGES = {71--80}, ISSN = {0010-2571}, MRCLASS = {14.0X}, MRNUMBER = {0010433 (6,17b)}, MRREVIEWER = {V. Snyder}, } @book {Fulton, AUTHOR = {Fulton, William}, TITLE = {Intersection theory}, SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]}, VOLUME = {2}, PUBLISHER = {Springer-Verlag, Berlin}, YEAR = {1984}, PAGES = {xi+470}, ISBN = {3-540-12176-5}, MRCLASS = {14C17 (14-02 14C40)}, MRNUMBER = {732620 (85k:14004)}, MRREVIEWER = {Werner Kleinert}, DOI = {10.1007/978-3-662-02421-8}, URL = {http://dx.doi.org/10.1007/978-3-662-02421-8}, } @misc {GalShi, AUTHOR = {Galkin, Sergey and Shinder, Evgeny}, TITLE = {The {F}ano variety of lines and rationality problem for a cubic hypersurface}, NOTE = {arXiv:1405.5154}, YEAR = {2014}, } @article {HaJAG, AUTHOR = {Hassett, Brendan}, TITLE = {Some rational cubic fourfolds}, JOURNAL = {J. Algebraic Geom.}, FJOURNAL = {Journal of Algebraic Geometry}, VOLUME = {8}, YEAR = {1999}, NUMBER = {1}, PAGES = {103--114}, ISSN = {1056-3911}, MRCLASS = {14J35 (14C30 14E08 14M20)}, MRNUMBER = {1658216 (2000a:14046)}, MRREVIEWER = {Kristian Ranestad}, } @article {HaCM, AUTHOR = {Hassett, Brendan}, TITLE = {Special cubic fourfolds}, JOURNAL = {Compositio Math.}, FJOURNAL = {Compositio Mathematica}, VOLUME = {120}, YEAR = {2000}, NUMBER = {1}, PAGES = {1--23}, ISSN = {0010-437X}, CODEN = {CMPMAF}, MRCLASS = {14J35 (14J10 14J28 14J45)}, MRNUMBER = {1738215 (2001g:14066)}, MRREVIEWER = {Elham Izadi}, DOI = {10.1023/A:1001706324425}, URL = {http://dx.doi.org/10.1023/A:1001706324425}, } @article {HTGAFA, AUTHOR = {Hassett, B. and Tschinkel, Y.}, TITLE = {Rational curves on holomorphic symplectic fourfolds}, JOURNAL = {Geom. Funct. Anal.}, FJOURNAL = {Geometric and Functional Analysis}, VOLUME = {11}, YEAR = {2001}, NUMBER = {6}, PAGES = {1201--1228}, ISSN = {1016-443X}, CODEN = {GFANFB}, MRCLASS = {14J35 (14C20 32J18)}, MRNUMBER = {1878319 (2002m:14033)}, MRREVIEWER = {Mark Gross}, DOI = {10.1007/s00039-001-8229-1}, URL = {http://dx.doi.org/10.1007/s00039-001-8229-1}, } @article {HTGAFA2, AUTHOR = {Hassett, Brendan and Tschinkel, Yuri}, TITLE = {Moving and ample cones of holomorphic symplectic fourfolds}, JOURNAL = {Geom. Funct. Anal.}, FJOURNAL = {Geometric and Functional Analysis}, VOLUME = {19}, YEAR = {2009}, NUMBER = {4}, PAGES = {1065--1080}, ISSN = {1016-443X}, CODEN = {GFANFB}, MRCLASS = {14J35 (14C05 14C20)}, MRNUMBER = {2570315 (2011c:14119)}, MRREVIEWER = {Ilya Karzhemanov}, DOI = {10.1007/s00039-009-0022-6}, URL = {http://dx.doi.org/10.1007/s00039-009-0022-6}, } @article {HVAV, AUTHOR = {Hassett, Brendan and V{\'a}rilly-Alvarado, Anthony and Varilly, Patrick}, TITLE = {Transcendental obstructions to weak approximation on general {K}3 surfaces}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {228}, YEAR = {2011}, NUMBER = {3}, PAGES = {1377--1404}, ISSN = {0001-8708}, CODEN = {ADMTA4}, MRCLASS = {14F22 (11G35 14C22 14J20 14J28)}, MRNUMBER = {2824558 (2012i:14025)}, MRREVIEWER = {I. Dolgachev}, DOI = {10.1016/j.aim.2011.06.017}, URL = {http://dx.doi.org/10.1016/j.aim.2011.06.017}, } @incollection {HLOY, AUTHOR = {Hosono, Shinobu and Lian, Bong H. and Oguiso, Keiji and Yau, Shing-Tung}, TITLE = {Fourier-{M}ukai partners of a {$K3$} surface of {P}icard number one}, BOOKTITLE = {Vector bundles and representation theory ({C}olumbia, {MO}, 2002)}, SERIES = {Contemp. Math.}, VOLUME = {322}, PAGES = {43--55}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = {2003}, MRCLASS = {14J28 (18E30)}, MRNUMBER = {1987738 (2004b:14065)}, MRREVIEWER = {Bal{\'a}zs Szendr{\"o}i}, DOI = {10.1090/conm/322/05678}, URL = {http://dx.doi.org/10.1090/conm/322/05678}, } @article {HLOY2, AUTHOR = {Hosono, Shinobu and Lian, Bong H. and Oguiso, Keiji and Yau, Shing-Tung}, TITLE = {Autoequivalences of derived category of a {$K3$} surface and monodromy transformations}, JOURNAL = {J. Algebraic Geom.}, FJOURNAL = {Journal of Algebraic Geometry}, VOLUME = {13}, YEAR = {2004}, NUMBER = {3}, PAGES = {513--545}, ISSN = {1056-3911}, MRCLASS = {14J28 (18E30)}, MRNUMBER = {2047679 (2005f:14076)}, MRREVIEWER = {Bal{\'a}zs Szendr{\H{o}}i}, DOI = {10.1090/S1056-3911-04-00364-9}, URL = {http://dx.doi.org/10.1090/S1056-3911-04-00364-9}, } @article {HuKl, AUTHOR = {Hulek, Klaus and Kloosterman, Remke}, TITLE = {The {$L$}-series of a cubic fourfold}, JOURNAL = {Manuscripta Math.}, FJOURNAL = {Manuscripta Mathematica}, VOLUME = {124}, YEAR = {2007}, NUMBER = {3}, PAGES = {391--407}, ISSN = {0025-2611}, CODEN = {MSMHB2}, MRCLASS = {11G40 (14G10 14G25 14J35)}, MRNUMBER = {2350552 (2008h:11067)}, MRREVIEWER = {Noriko Yui}, DOI = {10.1007/s00229-007-0121-3}, URL = {http://dx.doi.org/10.1007/s00229-007-0121-3}, } @article {HuyInv, AUTHOR = {Huybrechts, Daniel}, TITLE = {Compact hyper-{K}\"ahler manifolds: basic results}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {135}, YEAR = {1999}, NUMBER = {1}, PAGES = {63--113}, ISSN = {0020-9910}, CODEN = {INVMBH}, MRCLASS = {32J27 (14J40 32G20 32Q15 53C26)}, MRNUMBER = {1664696 (2000a:32039)}, MRREVIEWER = {I. Dolgachev}, DOI = {10.1007/s002220050280}, URL = {http://dx.doi.org/10.1007/s002220050280}, } @article {Kul, AUTHOR = {Kulikov, Vik. S.}, TITLE = {A remark on the nonrationality of a generic cubic fourfold}, JOURNAL = {Mat. Zametki}, FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Matematicheskie Zametki}, VOLUME = {83}, YEAR = {2008}, NUMBER = {1}, PAGES = {61--68}, ISSN = {0025-567X}, MRCLASS = {14J35 (14C30 14E08)}, MRNUMBER = {2399998 (2009b:14075)}, MRREVIEWER = {Adrian Langer}, DOI = {10.1134/S0001434608010070}, URL = {http://dx.doi.org/10.1134/S0001434608010070}, } @incollection {Kuz08, AUTHOR = {Kuznetsov, Alexander}, TITLE = {Derived categories of cubic fourfolds}, BOOKTITLE = {Cohomological and geometric approaches to rationality problems}, SERIES = {Progr. Math.}, VOLUME = {282}, PAGES = {219--243}, PUBLISHER = {Birkh\"auser Boston, Inc., Boston, MA}, YEAR = {2010}, MRCLASS = {14F05 (14E05)}, MRNUMBER = {2605171 (2011c:14049)}, MRREVIEWER = {Paolo Stellari}, DOI = {10.1007/978-0-8176-4934-0_9}, URL = {http://dx.doi.org/10.1007/978-0-8176-4934-0_9}, } @misc {Kuz15, AUTHOR = {Kuznetsov, Alexander}, TITLE = {Derived categories view on rationality problems}, NOTE = {arXiv:1509.09115}, HOWPUBLISHED = {Lecture notes for the CIME--CIRM summer school, Levico Terme}, YEAR = {2015}, } @article {LazaAnnals, AUTHOR = {Laza, Radu}, TITLE = {The moduli space of cubic fourfolds via the period map}, JOURNAL = {Ann. of Math. (2)}, FJOURNAL = {Annals of Mathematics. Second Series}, VOLUME = {172}, YEAR = {2010}, NUMBER = {1}, PAGES = {673--711}, ISSN = {0003-486X}, CODEN = {ANMAAH}, MRCLASS = {14J10 (14C34 32G20)}, MRNUMBER = {2680429 (2011m:14059)}, MRREVIEWER = {Francesco Polizzi}, DOI = {10.4007/annals.2010.172.673}, URL = {http://dx.doi.org/10.4007/annals.2010.172.673}, } ` @article {LLSvS, AUTHOR = {Lehn, Christian and Lehn, Manfred and Sorger, Christoph and van Straten, Duco}, TITLE = {Twisted cubics on cubic fourfolds}, JOURNAL = {J. Reine Angew. Math.}, FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's Journal]}, YEAR = {2015}, ISSN = {0075-4102}, DOI = {10.1515/crelle-2014-0144}, URL = {http://dx.doi.org/10.1515/crelle-2014-0144}, } @article {LZ, AUTHOR = {Li, Zhiyuan and Zhang, Letao}, TITLE = {Modular forms and special cubic fourfolds}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {245}, YEAR = {2013}, PAGES = {315--326}, ISSN = {0001-8708}, MRCLASS = {14H10 (11F03)}, MRNUMBER = {3084431}, MRREVIEWER = {M. S. Mahadeva Naika}, DOI = {10.1016/j.aim.2013.06.003}, URL = {http://dx.doi.org/10.1016/j.aim.2013.06.003}, } @article {Loo, AUTHOR = {Looijenga, Eduard}, TITLE = {The period map for cubic fourfolds}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {177}, YEAR = {2009}, NUMBER = {1}, PAGES = {213--233}, ISSN = {0020-9910}, CODEN = {INVMBH}, MRCLASS = {32G20 (14J35 14J45 14L24 32N15)}, MRNUMBER = {2507640 (2010h:32013)}, MRREVIEWER = {I. Dolgachev}, DOI = {10.1007/s00222-009-0178-6}, URL = {http://dx.doi.org/10.1007/s00222-009-0178-6}, } @article {MacSte, AUTHOR = {Macr{\`{\i}}, Emanuele and Stellari, Paolo}, TITLE = {Fano varieties of cubic fourfolds containing a plane}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {354}, YEAR = {2012}, NUMBER = {3}, PAGES = {1147--1176}, ISSN = {0025-5831}, MRCLASS = {14J45 (14E05 14J60)}, MRNUMBER = {2983083}, MRREVIEWER = {Zhiyu Tian}, DOI = {10.1007/s00208-011-0776-7}, URL = {http://dx.doi.org/10.1007/s00208-011-0776-7}, } @incollection {MarkSurv, AUTHOR = {Markman, Eyal}, TITLE = {A survey of {T}orelli and monodromy results for holomorphic-symplectic varieties}, BOOKTITLE = {Complex and differential geometry}, SERIES = {Springer Proc. Math.}, VOLUME = {8}, PAGES = {257--322}, PUBLISHER = {Springer, Heidelberg}, YEAR = {2011}, MRCLASS = {14D07 (14J15 32G20 53C26)}, MRNUMBER = {2964480}, MRREVIEWER = {Kieran G. O'Grady}, DOI = {10.1007/978-3-642-20300-8_15}, URL = {http://dx.doi.org/10.1007/978-3-642-20300-8_15}, } @misc {Maya, AUTHOR = {Mayanskiy, Evgeny}, TITLE = {Intersection lattices of cubic fourfolds}, YEAR = {2011}, NOTE = {arXiv:1112.0806}, } @article {Morin, AUTHOR = {Morin, Ugo}, TITLE = {Sulla razionalit\`a dell'ipersuperficie cubica generale dello spazio lineare {$S_5$}}, JOURNAL = {Rend. Sem. Mat. Univ. Padova}, FJOURNAL = {Rendiconti del Seminario Matematico della Universit\`a di Padova. The Mathematical Journal of the University of Padova}, VOLUME = {11}, YEAR = {1940}, PAGES = {108--112}, ISSN = {0041-8994}, MRCLASS = {14.0X}, MRNUMBER = {0020273 (8,527e)}, MRREVIEWER = {A. Seidenberg}, } @incollection {MukaiTata, AUTHOR = {Mukai, S.}, TITLE = {On the moduli space of bundles on {$K3$} surfaces. {I}}, BOOKTITLE = {Vector bundles on algebraic varieties ({B}ombay, 1984)}, SERIES = {Tata Inst. Fund. Res. Stud. Math.}, VOLUME = {11}, PAGES = {341--413}, PUBLISHER = {Tata Inst. Fund. Res., Bombay}, YEAR = {1987}, MRCLASS = {14J28 (14D22 14F05)}, MRNUMBER = {893604 (88i:14036)}, MRREVIEWER = {Mei Chu Chang}, } @book {MFK, AUTHOR = {Mumford, D. and Fogarty, J. and Kirwan, F.}, TITLE = {Geometric invariant theory}, SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related Areas (2)]}, VOLUME = {34}, EDITION = {Third}, PUBLISHER = {Springer-Verlag, Berlin}, YEAR = {1994}, PAGES = {xiv+292}, ISBN = {3-540-56963-4}, MRCLASS = {14D25 (58E05 58F05)}, MRNUMBER = {1304906 (95m:14012)}, MRREVIEWER = {Yi Hu}, DOI = {10.1007/978-3-642-57916-5}, URL = {http://dx.doi.org/10.1007/978-3-642-57916-5}, } @article {Nik, AUTHOR = {Nikulin, V. V.}, TITLE = {Integer symmetric bilinear forms and some of their geometric applications}, JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.}, FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya}, VOLUME = {43}, YEAR = {1979}, NUMBER = {1}, PAGES = {111--177, 238}, ISSN = {0373-2436}, MRCLASS = {10C05 (14G30 14J17 14J25 57M99 57R45 58C27)}, MRNUMBER = {525944 (80j:10031)}, MRREVIEWER = {I. Dolgachev}, } @misc {Nuer, AUTHOR = {Nuer, Howard}, TITLE = {Unirationality of moduli spaces of special cubic fourfolds and {$K3$} surfaces}, NOTE = {arXiv:1503.05256v1}, YEAR = {2015}, } @article {Orlov, AUTHOR = {Orlov, D. O.}, TITLE = {Equivalences of derived categories and {$K3$} surfaces}, NOTE = {Algebraic geometry, 7}, JOURNAL = {J. Math. Sci. (New York)}, FJOURNAL = {Journal of Mathematical Sciences (New York)}, VOLUME = {84}, YEAR = {1997}, NUMBER = {5}, PAGES = {1361--1381}, ISSN = {1072-3374}, CODEN = {JMTSEW}, MRCLASS = {14J28 (14F05 18E30)}, MRNUMBER = {1465519 (99a:14054)}, MRREVIEWER = {Jong Hae Keum}, DOI = {10.1007/BF02399195}, URL = {http://dx.doi.org/10.1007/BF02399195}, } @phdthesis {RanThesis, AUTHOR = {Ranestad, Kristian}, TITLE = {On smooth surfaces of degree 10 in the projective fourspace}, SCHOOL = {University of Oslo}, YEAR = {1988}, } @incollection {RanPaper, AUTHOR = {Ranestad, Kristian}, TITLE = {Surfaces of degree {$10$} in the projective fourspace}, BOOKTITLE = {Problems in the theory of surfaces and their classification ({C}ortona, 1988)}, SERIES = {Sympos. Math., XXXII}, PAGES = {271--307}, PUBLISHER = {Academic Press, London}, YEAR = {1991}, MRCLASS = {14C05 (14J10)}, MRNUMBER = {1273383}, MRREVIEWER = {James E. Alexander}, } @article {ST, AUTHOR = {Seidel, Paul and Thomas, Richard}, TITLE = {Braid group actions on derived categories of coherent sheaves}, JOURNAL = {Duke Math. J.}, FJOURNAL = {Duke Mathematical Journal}, VOLUME = {108}, YEAR = {2001}, NUMBER = {1}, PAGES = {37--108}, ISSN = {0012-7094}, CODEN = {DUMJAO}, MRCLASS = {14F05 (14J32 18E30 20F36 53D40)}, MRNUMBER = {1831820 (2002e:14030)}, MRREVIEWER = {Mikhail G. Khovanov}, DOI = {10.1215/S0012-7094-01-10812-0}, URL = {http://dx.doi.org/10.1215/S0012-7094-01-10812-0}, } @article {Siu, AUTHOR = {Siu, Yum Tong}, TITLE = {A simple proof of the surjectivity of the period map of {$K3$}\ surfaces}, JOURNAL = {Manuscripta Math.}, FJOURNAL = {Manuscripta Mathematica}, VOLUME = {35}, YEAR = {1981}, NUMBER = {3}, PAGES = {311--321}, ISSN = {0025-2611}, CODEN = {MSMHB2}, MRCLASS = {14J15 (14J25)}, MRNUMBER = {636458 (83g:14015)}, MRREVIEWER = {Yukihiko Namikawa}, DOI = {10.1007/BF01263265}, URL = {http://dx.doi.org/10.1007/BF01263265}, } @article {Swan, AUTHOR = {Swan, Richard G.}, TITLE = {Zero cycles on quadric hypersurfaces}, JOURNAL = {Proc. Amer. Math. Soc.}, FJOURNAL = {Proceedings of the American Mathematical Society}, VOLUME = {107}, YEAR = {1989}, NUMBER = {1}, PAGES = {43--46}, ISSN = {0002-9939}, CODEN = {PAMYAR}, MRCLASS = {14C25 (11E04)}, MRNUMBER = {979219 (89m:14005)}, MRREVIEWER = {Wayne Raskind}, DOI = {10.2307/2048032}, URL = {http://dx.doi.org/10.2307/2048032}, } @misc {TVA, AUTHOR = {Tanimoto, Sho and V\'arilly-Alvarado, Anthony}, TITLE = {Kodaira dimension of moduli of special cubic fourfolds}, NOTE = {arXiv:1509.01562v1}, YEAR = {2015}, } @article {Tregub1, AUTHOR = {Tregub, S. L.}, TITLE = {Three constructions of rationality of a cubic fourfold}, JOURNAL = {Vestnik Moskov. Univ. Ser. I Mat. Mekh.}, FJOURNAL = {Vestnik Moskovskogo Universiteta. Seriya I. Matematika, Mekhanika}, YEAR = {1984}, NUMBER = {3}, PAGES = {8--14}, ISSN = {0201-7385}, MRCLASS = {14J35 (14E05)}, MRNUMBER = {749015 (86a:14041)}, MRREVIEWER = {Werner Kleinert}, } @article {Tregub2, AUTHOR = {Tregub, S. L.}, TITLE = {Two remarks on four-dimensional cubics}, JOURNAL = {Uspekhi Mat. Nauk}, FJOURNAL = {Rossi\u\i skaya Akademiya Nauk. Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk}, VOLUME = {48}, YEAR = {1993}, NUMBER = {2(290)}, PAGES = {201--202}, ISSN = {0042-1316}, MRCLASS = {14J35}, MRNUMBER = {1239880 (95a:14041)}, MRREVIEWER = {A. S. Tikhomirov}, DOI = {10.1070/RM1993v048n02ABEH003729}, URL = {http://dx.doi.org/10.1070/RM1993v048n02ABEH003729}, } @article {vanGeemen, AUTHOR = {van Geemen, Bert}, TITLE = {Some remarks on {B}rauer groups of {$K3$} surfaces}, JOURNAL = {Adv. Math.}, FJOURNAL = {Advances in Mathematics}, VOLUME = {197}, YEAR = {2005}, NUMBER = {1}, PAGES = {222--247}, ISSN = {0001-8708}, CODEN = {ADMTA4}, MRCLASS = {14F22 (14E20 14J27 14J28)}, MRNUMBER = {2166182 (2006h:14025)}, MRREVIEWER = {Tihomir A. Petrov}, DOI = {10.1016/j.aim.2004.10.004}, URL = {http://dx.doi.org/10.1016/j.aim.2004.10.004}, } @article {Voisin86, AUTHOR = {Voisin, Claire}, TITLE = {Th\'eor\`eme de {T}orelli pour les cubiques de {${\bf P}^5$}}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {86}, YEAR = {1986}, NUMBER = {3}, PAGES = {577--601}, ISSN = {0020-9910}, CODEN = {INVMBH}, MRCLASS = {14C30 (14J35)}, MRNUMBER = {860684 (88g:14006)}, MRREVIEWER = {Fabio Bardelli}, DOI = {10.1007/BF01389270}, URL = {http://dx.doi.org/10.1007/BF01389270}, } @article {VoisinJJM, AUTHOR = {Voisin, Claire}, TITLE = {Some aspects of the {H}odge conjecture}, JOURNAL = {Jpn. J. Math.}, FJOURNAL = {Japanese Journal of Mathematics}, VOLUME = {2}, YEAR = {2007}, NUMBER = {2}, PAGES = {261--296}, ISSN = {0289-2316}, MRCLASS = {14C30 (32J25)}, MRNUMBER = {2342587 (2008g:14012)}, MRREVIEWER = {James D. Lewis}, DOI = {10.1007/s11537-007-0639-x}, URL = {http://dx.doi.org/10.1007/s11537-007-0639-x}, } @article {VoisinJAG, AUTHOR = {Voisin, Claire}, TITLE = {Abel-{J}acobi map, integral {H}odge classes and decomposition of the diagonal}, JOURNAL = {J. Algebraic Geom.}, FJOURNAL = {Journal of Algebraic Geometry}, VOLUME = {22}, YEAR = {2013}, NUMBER = {1}, PAGES = {141--174}, ISSN = {1056-3911}, MRCLASS = {14C30 (14C15 14M22)}, MRNUMBER = {2993050}, MRREVIEWER = {Fumio Hazama}, DOI = {10.1090/S1056-3911-2012-00597-9}, URL = {http://dx.doi.org/10.1090/S1056-3911-2012-00597-9}, } @misc {VoisinSDG, AUTHOR = {Voisin, Claire}, TITLE = {Stable birational invariants and the {L}\"uroth problem}, YEAR = {2015}, NOTE = {Preprint at \url{http://webusers.imj-prg.fr/~claire.voisin/}}, } @article {VoisinJEMS, AUTHOR = {Voisin, Claire}, TITLE = {On the universal {$\CH_0$} group of cubic hypersurfaces}, JOURNAL = {J. Eur. Math. Soc. (JEMS)}, FJOURNAL = {Journal of the European Mathematical Society (JEMS)}, NOTE = {To appear, arXiv:1407.7261v2}, YEAR = {2014}, } @article {VoisinIM, AUTHOR = {Voisin, Claire}, TITLE = {Unirational threefolds with no universal codimension {$2$} cycle}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {201}, YEAR = {2015}, NUMBER = {1}, PAGES = {207--237}, ISSN = {0020-9910}, MRCLASS = {14M20}, MRNUMBER = {3359052}, DOI = {10.1007/s00222-014-0551-y}, URL = {http://dx.doi.org/10.1007/s00222-014-0551-y}, } @misc {Voisin15, AUTHOR = {Voisin, Claire}, TITLE = {({S}table) rationality is not deformation invariant}, NOTE = {arXiv:1511.03591}, YEAR = {2015}, } @article {Wlo, AUTHOR = {W{\l}odarczyk, Jaros{\l}aw}, TITLE = {Toroidal varieties and the weak factorization theorem}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {154}, YEAR = {2003}, NUMBER = {2}, PAGES = {223--331}, ISSN = {0020-9910}, CODEN = {INVMBH}, MRCLASS = {14M25 (14E05 14E15)}, MRNUMBER = {2013783 (2004m:14113)}, MRREVIEWER = {Dan Abramovich}, DOI = {10.1007/s00222-003-0305-8}, URL = {http://dx.doi.org/10.1007/s00222-003-0305-8}, } @misc {Yoshioka99, AUTHOR = {Yoshioka, K{\=o}ta}, TITLE = {Irreducibility of moduli spaces of vector bundles on {$K3$} surfaces}, YEAR = {2000}, NOTE = {arXiv:9907001v2}, } @article {YoMA, AUTHOR = {Yoshioka, K{\=o}ta}, TITLE = {Moduli spaces of stable sheaves on abelian surfaces}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {321}, YEAR = {2001}, NUMBER = {4}, PAGES = {817--884}, ISSN = {0025-5831}, CODEN = {MAANA}, MRCLASS = {14D20 (14D22)}, MRNUMBER = {1872531 (2002k:14020)}, MRREVIEWER = {Jean-Marc Drezet}, DOI = {10.1007/s002080100255}, URL = {http://dx.doi.org/10.1007/s002080100255}, }