- Stable rationality in smooth families of threefolds
(with Andrew Kresch and Yuri Tschinkel)
dvi,
ps, or
pdf
- Cubic fourfolds fibered in sextic del Pezzo surfaces
(with Nicolas Addington, Yuri Tschinkel, and Anthony Várilly-Alvarado)
dvi,
ps, or
pdf

- A very general quartic double fourfold is not stably rational
(with Alena Pirutka and Yuri Tschinkel)
dvi,
ps, or
pdf

to appear in*Algebraic geometry* - On stable rationality of Fano threefolds and del Pezzo fibrations
(with Yuri Tschinkel)
dvi,
ps, or
pdf

to appear in*Journal für die reine und angewandte Mathematik* - Intersections of three quadrics in
**P**^{7}(with Alena Pirutka and Yuri Tschinkel) dvi, ps, or pdf

*Surveys in Differential Geometry*,**22**, No. 1 (2017), 259-274. - Stable rationality of quadric surface bundles over surfaces
(with Alena Pirutka and Yuri Tschinkel)
dvi,
ps, or
pdf

*Acta Mathematica***220**(2018), no. 2, 341-365 - Cremona transformations and derived equivalences of K3 surfaces
(with Kuan-Wen Lai)
dvi,
ps, or
pdf

*Compositio Mathematica***154**(2018), no. 7, 1508-1533 - Cubic fourfolds, K3 surfaces, and rationality questions
dvi,
ps, or
pdf

*Rationality Problems in Algebraic Geometry*, R. Pardini and G.P. Pirola, eds., 26-66,

CIME Foundation Subseries, Lecture Notes in Mathematics**2172**, Springer 2016 - Rational points on K3 surfaces and derived equivalence (with Yuri Tschinkel)
dvi,
ps, or
pdf

*Brauer groups and obstruction problems: moduli spaces and arithmetic*,

A. Auel, B. Hassett, A. Várilly-Alvarado, and B. Viray, eds., 87-113, Progress in Mathematics**320**, Springer 2017 - Stable rationality and conic bundles (with Andrew Kresch and Yuri Tschinkel)
dvi,
ps, or
pdf

*Mathematische Annalen***365**(2016), no. 3-4, 1201-1217 - On the moduli of degree 4 Del Pezzo surfaces (with Andrew Kresch and Yuri
Tschinkel)
dvi,
ps, or
pdf

*Development of Moduli Theory -- Kyoto 2013*, O. Fujino, S. Kondô, A. Moriwaki, M.-H. Saito and K. Yoshioka eds.,

349-386, Advanced Studies in Pure Mathematics**69**, Mathematical Society of Japan, 2016 - Extremal rays and automorphisms of holomorphic symplectic
varieties (with Yuri Tschinkel)
dvi,
ps, or
pdf

*K3 surfaces and their Moduli*, proceedings of a 2014 conference at Schiermonnikoog, The Netherlands, C. Faber, G. Farkas, and G. van der Geer eds.,

73-95, Progress in mathematics**315**, Birkhhäuser, 2016 - Mori cones of holomorphic symplectic varieties of K3 type (with Arend Bayer and
Yuri Tschinkel)
dvi,
ps, or
pdf

*Annales scientifiques de l'École normale supérieure***48**, fasc. 4 (2015), 941-950 - Balanced line bundles and equivariant compactifications of homogeneous spaces (with Sho Tanimoto and Yuri Tschinkel)
dvi,
ps, or
pdf

*International Mathematics Research Notices***2015**, no. 15, 6375-6410 - Embedding pointed curves in K3 surfaces (with Yuri Tschinkel)
dvi,
ps, or
pdf

*Mathematische Zeitschrift***278**(2014), no. 3, 927-953 - Rational curves on K3 surfaces
dvi,
ps, or
pdf

Notes from a summer school in Grenoble, June 2010 - Quartic del Pezzo surfaces over function fields of curves (with Yuri Tschinkel)
dvi,
ps, or
pdf

*Central European Journal of Mathematics***13**(2014), no. 3, 395-420 - Failure of the Hasse principle on general K3 surfaces (with Anthony Várilly-Alvarado)
dvi,
ps, or
pdf

*Journal of the Institute of Mathematics of Jussieu***12**(2013), no. 4, 853-877 - Log minimal model program for the moduli space of curves:
The first flip (with Donghoon Hyeon)
dvi,
ps, or
pdf

*Annals of Mathematics***177**(2013), no. 3, 911-968 - Effective computation of Picard groups and Brauer-Manin obstructions of degree two

K3 surfaces over number fields (with Andrew Kresch and Yuri Tschinkel) dvi, ps, or pdf

*Rendiconti del Circolo Matematico di Palermo***62**(2013), no. 1, 137-151 - Hodge theory and Lagrangian planes on generalized Kummer fourfolds (with Yuri Tschinkel)
dvi,
ps, or
pdf

*Moscow Mathematical Journal***13**(2013), no. 1, 33–56 - Spaces of sections of quadric surface fibrations over curves (with Yuri Tschinkel)
dvi,
ps, or
pdf

*Compact Moduli Spaces and Vector Bundles*, proceedings of the 2010 conference at the

University of Georgia, V. Alexeev et al. eds., Contemporary Mathematics**564**, 227-249,

American Mathematical Society, Providence, 2012 - Characterizing projective spaces on deformations of Hilbert schemes of
K3 surfaces
(with David Harvey and Yuri Tschinkel)
dvi,
ps, or
pdf

*Communications on Pure and Applied Mathematics***65**(2012), no.2, 264-286 - Transcendental obstructions to weak approximation
on general K3 surfaces (with Anthony Várilly-Alvarado and Patrick Varilly)
dvi,
ps, or
pdf

*Advances in Mathematics***228**(2011), no. 3, 1377-1404 - Constructing rational curves on K3 surfaces (with Fedor Bogomolov and
Yuri Tschinkel)
dvi,
ps, or
pdf

*Duke Mathematical Journal***157**(2011), no. 3, 535-550 - Stable varieties with a twist (with Dan Abramovich)
dvi,
ps, or
pdf

*Classification of algebraic varieties*, proceedings of the 2009 conference at Schiermonnikoog the Netherlands,

Carel Faber, Gerard van der Geer, and Eduard J.N. Looijenga eds., 1-38, European Mathematical Society, Zürich, 2011 - Weak approximation and rationally connected varieties over function fields of curves
dvi,
ps, or
pdf

in*Variétés rationnellement connexes : aspects géométriques et arithmétiques*,

Panoramas et Synthèses**31**(2010), 115-153, Société Mathématique de France - Intersection numbers of extremal rays on holomorphic symplectic
varieties (with
Yuri Tschinkel)
dvi,
ps, or
pdf

*Asian Journal of Mathematics***14**(2010), no. 3, 303-322 - Flops on holomorphic symplectic fourfolds
and determinantal cubic hypersurfaces (with Yuri Tschinkel)
dvi,
ps, or
pdf

*Journal of the Institute of Mathematics of Jussieu***9**(2010), no. 1, 125-153 - Stability computation via Gröbner bases (with Donghoon Hyeon and Yongnam Lee)
dvi,
ps, or
pdf

*Journal of the Korean Mathematical Society***47**(2010), no. 1, 41-62 - Rational surfaces over nonclosed fields
dvi,
ps, or
pdf

*Arithmetic Geometry*, proceedings of the 2006 Clay Mathematics Institute Summer School,

Clay Mathematics Proceedings**8**155-210, American Mathematics Society, Providence, 2009 - Moving and ample cones of holomorphic symplectic fourfolds (with Yuri Tschinkel)
dvi,
ps, or
pdf

*Geometric and Functional Analysis***19**(2009), no. 4, 1065-1080 -
Log canonical models for the moduli space of curves:
The first divisorial contraction (with Donghoon Hyeon)
dvi, ps,
or pdf

*Transactions of the AMS***361**(2009), 4471-4489 -
Weak approximation for hypersurfaces of low degree (with Yuri Tschinkel)
dvi, ps,
or pdf

*Algebraic Geometry-Seattle 2005*, D. Abramovich et al. eds.,

Proceedings of Symposia in Pure Mathematics,**80**, no. 2, 937-955,

American Mathematical Society, Providence, 2009 -
Potential density of rational points for K3 surfaces over function
fields (with Yuri Tschinkel)
dvi, ps,
or pdf

*American Journal of Mathematics****130**(2008), no. 5, 1263-1278 -
Log Fano varieties over function fields of curves (with Yuri Tschinkel)
dvi, ps,
or pdf

*Inventiones mathematicae***173**(2008), no. 1, 7-21 -
Approximation at places of bad reduction for rationally
connected varieties (with Yuri Tschinkel)
dvi, ps,
or pdf

*Pure and Applied Mathematics Quarterly***4**(2008), no. 3, 743-766 -
Weak approximation over function fields (with Yuri Tschinkel)
dvi, ps,
or pdf

*Inventiones mathematicae*****163**(2006), 171-190 -
Classical and minimal models of the moduli space of curves of genus two
dvi, ps,
or pdf

*Geometric methods in algebra and number theory*, F. Bogomolov and Y. Tschinkel eds.,

169-192, Progress in mathematics**235**, Birkhhäuser, Boston, 2005 -
Equations of universal torsors and Cox rings
(notes by Ulrich Derenthal)
dvi,
ps, or
pdf

Mathematisches Institut, Georg-August-Universität Göttingen: Seminars Summer Term 2004,

135--143, Universitätsdrucke Göttingen, Göttingen, 2004 -
Universal torsors and Cox rings
(with Yuri Tschinkel)
dvi, ps,
or pdf

*Arithmetic of higher-dimensional algebraic varieties*, B. Poonen and Y. Tschinkel eds., 149-173,

Progress in mathematics**226**, Birkhhäuser, Boston, 2004 -
Reflexive pull-backs and base extension (with Sándor Kovács)
dvi, ps, or
pdf

*Journal of Algebraic Geometry***13**(2004), 233-247 -
Integral points and effective cones of moduli spaces of
stable maps (with Yuri Tschinkel)
dvi, ps, or
pdf

*Duke Mathematical Journal***120**(2003), no. 3, 577-599

Erratum dvi, ps, or pdf -
Potential density of rational points on algebraic varieties,
dvi,
ps , or
pdf
*Higher Dimensional Varieties and Rational Points,*K.J. Böröczky, J. Kollár, T. Szamuely eds.,

Bolyai Society Mathematical Studies, Vol. 12, Springer Verlag, Heidelberg, 2003 -
Moduli spaces of weighted pointed stable curves
dvi, ps,
pdf

*Advances in Mathematics***173**(2003), Issue 2, 316-352 -
On the effective cone of the moduli space of pointed rational curves
(with Yuri Tschinkel)
dvi, ps, or
pdf

*Topology and Geometry: Commemorating SISTAG,*A.J. Berrick, M.C. Leung, and X.W. Xu eds.,

Contemporary mathematics**314**, 83-96, American Mathematical Society, Providence, 2002 -
The weak Lefschetz principle is false for ample cones
(with Hui-Wen Lin and Chin-Lung Wang)
dvi,
ps, or
pdf

*Asian Journal of Mathematics***6**(2002), No. 1, 95-100 -
Density of integral points on algebraic varieties
(with Yuri Tschinkel)
dvi, ps, or
pdf

*Rational Points on Algebraic Varieties*,

(Points rationnels des variétés algébriques, Luminy, 1999), 165-197,

Progress in mathematics**199**, Birkhhäuser, Boston, 2001 -
Rational curves on holomorphic symplectic fourfolds
(with Yuri Tschinkel)
dvi, ps, or pdf

*Geometric and Functional Analysis***11**(2001), no. 6, 1201-1228 -
Brauer groups and quotient stacks
(with Dan Edidin, Andrew Kresch, and Angelo Vistoli)
dvi, ps,
or pdf

*American Journal of Mathematics***123**(2001), no. 4, 761-777* -
Stable limits of log surfaces and Cohen-Macaulay singularities
dvi, ps,
or pdf

*Journal of Algebra***242**(2001), no. 1, 225-235 -
Abelian fibrations and rational points on symmetric products
(with Yuri Tschinkel)
dvi, ps,
or pdf

*International Journal of Mathematics***11**(2000), no. 9, 1163-1176 -
Local stable reduction of plane curve singularities
dvi, ps, or
pdf

*Journal für die reine und angewandte Mathematik***520**(2000), 169-194 -
Special cubic fourfolds (abridged version)
dvi, ps, or
pdf

*Compositio Mathematica***120**(2000), no. 1, 1-23 -
Geometry of equivariant compactifications of
**G**_{a}^{n}(with Yuri Tschinkel) dvi, ps, or pdf

*International Mathematical Research Notices***1999**, no. 22, 1211-1230 -
Stable log surfaces and limits of quartic plane curves
dvi,
ps, or
pdf

*manuscripta mathematica***100**(1999), 469-497 -
Some rational cubic fourfolds
dvi, ps, or
pdf

*Journal of Algebraic Geometry***8**(1999), 103-114 -
Correlation for surfaces of general type
dvi, ps, or
pdf

*Duke Mathematical Journal***85**(1996), no. 1, 95-107 -
Special cubic fourfolds (longwinded version)
dvi, ps, or
pdf

revision of*Special cubic hypersurfaces of dimension four*, Harvard University Thesis (1996)

*Copyright, The Johns Hopkins University Press

**The original publication is available at www.springerlink.com