Papers and Preprints

• Rationality of forms of M_0,n (with Yuri Tschinkel and Zhijia Zhang)

• Involutions on K3 surfaces and derived equivalence (with Yuri Tschinkel)

• Equivariant derived equivalence and rational points on K3 surfaces (with Yuri Tschinkel)
  Communications in Number Theory and Physics 17 (2023), no. 2, 293-312

• Torsors and stable equivariant birational geometry (with Yuri Tschinkel)
  Nagoya Mathematical Journal 250 (2023), 275-297

• Stable rationality in smooth families of threefolds (with Andrew Kresch and Yuri Tschinkel)
  Duke Mathematical Journal 172 (2023), no. 6, 1145-1172

• Reduction of Brauer classes on K3 surfaces, rationality, and derived equivalence (with Sarah Frei and Anthony Várilly-Alvarado)
  Journal für die reine und angewandte Mathematik 792 (2022), 289-305

• Equivariant geometry of odd-dimensional complete intersections of two quadrics (with Yuri Tschinkel)
  Pure and Applied Mathematics Quarterly 18 (2022), no. 4, 1555-1597

• Rationality of even-dimensional intersections of two real quadrics (with János Kollár and Yuri Tschinkel)
  Commentarii Mathematici Helvetici 97 (2022), no. 1, 183–207

• Symbols and equivariant birational geometry in small dimensions (with Andrew Kresch and Yuri Tschinkel)
  proceedings of the 2019 Schiermonnikoog conference `Rationality of varieties',
  G. Farkas, G. van der Geer, M. Shen, and L. Taelman eds., 201-236, Progress in Mathematics 342, Springer 2021

• Rationality of Fano threefolds of degree 18 over nonclosed fields (with Yuri Tschinkel) dvi, ps, or pdf
  proceedings of the 2019 Schiermonnikoog conference `Rationality of varieties',
  G. Farkas, G. van der Geer, M. Shen, and L. Taelman eds., 237-247, Progress in Mathematics 342, Springer 2021

• Rationality of complete intersections of two quadrics over nonclosed fields (with Yuri Tschinkel including an appendix by Jean-Louis Colliot-Thélène)
  L'Enseignement mathématique 67 (2021), no. 1-2, 1-44

• Cycle class maps and birational invariants (with Yuri Tschinkel) dvi, ps, or pdf
  Communications on Pure and Applied Mathematics 74 (2021), Issue 12, 2675-2698

• Varieties of planes on intersections of three quadrics (with Yuri Tschinkel) dvi, ps, or pdf
  European Journal of Mathematics 7 (2021), 613–632

• Cubic fourfolds fibered in sextic del Pezzo surfaces (with Nicolas Addington, Yuri Tschinkel, and Anthony Várilly-Alvarado) dvi, ps, or pdf
  American Journal of Mathematics 141 (2019), no. 6, 1479-1500

• On stable rationality of Fano threefolds and del Pezzo fibrations (with Yuri Tschinkel) dvi, ps, or pdf
  Journal für die reine und angewandte Mathematik 751 (2019), 275-287

• A very general quartic double fourfold is not stably rational (with Alena Pirutka and Yuri Tschinkel) dvi, ps, or pdf
  Algebraic geometry 6(1) (2019), 64-75

• Intersections of three quadrics in P⁷ (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_aⁿ (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