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, 293312

Torsors and stable equivariant birational geometry
(with Yuri Tschinkel)
Nagoya Mathematical Journal 250 (2023), 275297
 Stable rationality in smooth families of threefolds
(with Andrew Kresch and Yuri Tschinkel)
Duke Mathematical Journal
172 (2023), no. 6, 11451172

Reduction of Brauer classes on K3 surfaces, rationality, and
derived equivalence (with Sarah Frei and Anthony VárillyAlvarado)
Journal für die reine und angewandte Mathematik 792 (2022),
289305

Equivariant geometry of odddimensional complete intersections of two quadrics (with Yuri Tschinkel)
Pure and Applied Mathematics Quarterly 18 (2022), no. 4, 15551597
 Rationality of evendimensional
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.,
201236, 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., 237247, Progress in Mathematics 342, Springer 2021

Rationality of complete intersections of two quadrics over nonclosed fields (with
Yuri Tschinkel including an appendix by
JeanLouis ColliotThélène)
L'Enseignement mathématique 67 (2021), no. 12, 144
 Cycle class maps and birational invariants (with Yuri Tschinkel)
dvi,
ps, or
pdf
Communications on Pure and Applied Mathematics
74 (2021), Issue 12, 26752698
 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 VárillyAlvarado)
dvi,
ps, or
pdf
American Journal of Mathematics 141 (2019), no. 6, 14791500
 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), 275287
 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), 6475
 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), 259274.
 Stable rationality of quadric surface bundles over surfaces
(with Alena Pirutka and Yuri Tschinkel)
dvi,
ps, or
pdf
Acta Mathematica 220 (2018), no. 2, 341365
 Cremona transformations and derived equivalences of K3 surfaces
(with KuanWen Lai)
dvi,
ps, or
pdf
Compositio Mathematica 154 (2018), no. 7, 15081533
 Cubic fourfolds, K3 surfaces, and rationality questions
dvi,
ps, or
pdf
Rationality Problems in Algebraic Geometry,
R. Pardini and G.P. Pirola eds., 2666,
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. VárillyAlvarado, and B. Viray eds., 87113,
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. 34, 12011217
 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.,
349386, 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.,
7395, 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), 941950
 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, 63756410
 Embedding pointed curves in K3 surfaces (with Yuri Tschinkel)
dvi,
ps, or
pdf
Mathematische Zeitschrift 278 (2014), no. 3, 927953
 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, 395420
 Failure of the Hasse principle on general K3 surfaces (with Anthony VárillyAlvarado)
dvi,
ps, or
pdf
Journal of the Institute of Mathematics of Jussieu 12
(2013), no. 4, 853877
 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, 911968
 Effective computation of Picard groups and BrauerManin 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,
137151
 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, 227249,
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, 264286
 Transcendental obstructions to weak approximation
on general K3 surfaces (with Anthony VárillyAlvarado and Patrick Varilly)
dvi,
ps, or
pdf
Advances in Mathematics
228 (2011), no. 3, 13771404
 Constructing rational curves on K3 surfaces (with Fedor Bogomolov and
Yuri Tschinkel)
dvi,
ps, or
pdf
Duke Mathematical Journal 157 (2011), no. 3, 535550
 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., 138,
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), 115153,
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, 303322
 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, 125153
 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, 4162
 Rational surfaces over nonclosed fields
dvi,
ps, or
pdf
Arithmetic Geometry, proceedings of the 2006 Clay
Mathematics Institute Summer School,
Clay Mathematics Proceedings 8 155210,
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, 10651080

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), 44714489

Weak approximation for hypersurfaces of low degree (with Yuri Tschinkel)
dvi, ps,
or pdf
Algebraic GeometrySeattle 2005, D. Abramovich et al. eds.,
Proceedings of Symposia in Pure Mathematics,
80, no. 2, 937955,
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, 12631278

Log Fano varieties over function fields of curves (with Yuri Tschinkel)
dvi, ps,
or pdf
Inventiones mathematicae 173 (2008), no. 1, 721

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, 743766

Weak approximation over function fields (with Yuri Tschinkel)
dvi, ps,
or pdf
Inventiones mathematicae** 163 (2006), 171190

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.,
169192, Progress in mathematics 235, Birkhhäuser, Boston, 2005

Equations of universal torsors and Cox rings
(notes by Ulrich Derenthal)
dvi,
ps, or
pdf
Mathematisches Institut, GeorgAugustUniversität Göttingen: Seminars Summer Term 2004,
135143, Universitätsdrucke Göttingen, Göttingen, 2004

Universal torsors and Cox rings
(with Yuri Tschinkel)
dvi, ps,
or pdf
Arithmetic of higherdimensional algebraic varieties,
B. Poonen and Y. Tschinkel eds., 149173,
Progress in mathematics 226, Birkhhäuser, Boston, 2004

Reflexive pullbacks and base extension (with Sándor Kovács)
dvi, ps, or
pdf
Journal of Algebraic Geometry 13 (2004), 233247

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, 577599
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, 316352

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, 8396,
American Mathematical Society, Providence, 2002

The weak Lefschetz principle is false for ample cones
(with HuiWen Lin and ChinLung Wang)
dvi,
ps, or
pdf
Asian Journal of Mathematics 6 (2002), No. 1, 95100

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), 165197,
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, 12011228

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, 761777*

Stable limits of log surfaces and CohenMacaulay singularities
dvi, ps,
or pdf
Journal of Algebra
242 (2001), no. 1, 225235

Abelian fibrations and rational points on symmetric products
(with Yuri Tschinkel)
dvi, ps,
or pdf
International Journal of Mathematics 11 (2000), no. 9,
11631176

Local stable reduction of plane curve singularities
dvi, ps, or
pdf
Journal für die reine und angewandte
Mathematik
520 (2000), 169194

Special cubic fourfolds (abridged version)
dvi, ps, or
pdf
Compositio Mathematica 120 (2000), no. 1, 123

Geometry of equivariant compactifications of G_{a}^{n}
(with Yuri Tschinkel)
dvi, ps,
or pdf
International Mathematical Research Notices
1999 , no. 22, 12111230

Stable log surfaces and limits of quartic plane curves
dvi,
ps, or
pdf
manuscripta mathematica 100 (1999), 469497

Some rational cubic fourfolds
dvi, ps, or
pdf
Journal of Algebraic Geometry 8 (1999), 103114

Correlation for surfaces of general type
dvi, ps, or
pdf
Duke Mathematical Journal 85 (1996), no. 1, 95107

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