Witt rings, Pfister forms, and equivariant birational geometry arXiv HTML (with Yuri Tschinkel)
Moduli of conic surfaces over the line arXiv HTML(with Amanda Hernandez)
Degree two unirational parametrizations over the real field arXiv HTML (with Hayato Takagi and Sho Tanimoto), to appear in EMS Surveys in Mathematical Sciences
Cubic fourfolds of discriminant 24 and rationality arXiv HTML, to appear in Algebraic Geometry
Involutions on K3 surfaces and derived equivalence arXiv HTML (with Yuri Tschinkel), Mathematische Zeitschrift 312 (2026), no. 1, Paper No. 18
Equivariant geometry of low-dimensional quadrics arXiv HTML(with Yuri Tschinkel), Taiwanese Journal of Mathemathcs 29 (2025), no. 6, 1381-1402
Rationality of forms of M0,n (with Yuri Tschinkel and Zhijia Zhang), Journal of the London Mathematical Society 111 (2025), no. 2, Paper No. e70097
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), 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), Communications on Pure and Applied Mathematics 74 (2021), Issue 12, 2675-2698
Varieties of planes on intersections of three quadrics (with Yuri Tschinkel), 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), American Journal of Mathematics 141 (2019), no. 6, 1479-1500
On stable rationality of Fano threefolds and del Pezzo fibrations (with Yuri Tschinkel), 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), Algebraic geometry 6(1) (2019), 64-75
Intersections of three quadrics in P^7 (with Alena Pirutka and Yuri Tschinkel), Surveys in Differential Geometry 22, no. 1 (2017), 259-274.
Stable rationality of quadric surface bundles over surfaces (with Alena Pirutka and Yuri Tschinkel), Acta Mathematica 220 (2018), no. 2, 341-365
Cremona transformations and derived equivalences of K3 surfaces (with Kuan-Wen Lai), Compositio Mathematica154 (2018), no. 7, 1508-1533
Cubic fourfolds, K3 surfaces, and rationality questions, 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), 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), Mathematische Annalen 365 (2016), no. 3-4, 1201-1217
On the moduli of degree 4 Del Pezzo surfaces (with Andrew Kresch and Yuri Tschinkel), 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), 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), 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), International Mathematics Research Notices 2015, no. 15, 6375-6410
Embedding pointed curves in K3 surfaces (with Yuri Tschinkel), Mathematische Zeitschrift 278 (2014), no. 3, 927-953
Rational curves on K3 surfaces, Notes from a summer school in Grenoble, June 2010
Quartic del Pezzo surfaces over function fields of curves (with Yuri Tschinkel), Central European Journal of Mathematics 13 (2014), no. 3, 395-420
Failure of the Hasse principle on general K3 surfaces (with Anthony Várilly-Alvarado), 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), 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), Rendiconti del Circolo Matematico di Palermo 62 (2013), no. 1, 137-151
Hodge theory and Lagrangian planes on generalized Kummer fourfolds (with Yuri Tschinkel), Moscow Mathematical Journal 13 (2013), no. 1, 33–56
Spaces of sections of quadric surface fibrations over curves (with Yuri Tschinkel), 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), 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), Advances in Mathematics 228 (2011), no. 3, 1377-1404
Constructing rational curves on K3 surfaces (with Fedor Bogomolov and Yuri Tschinkel), Duke Mathematical Journal 157 (2011), no. 3, 535-550
Stable varieties with a twist (with Dan Abramovich), 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, 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), Asian Journal of Mathematics 14 (2010), no. 3, 303-322
Flops on holomorphic symplectic fourfolds and determinantal cubic hypersurfaces (with Yuri Tschinkel), 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), Journal of the Korean Mathematical Society 47 (2010), no. 1, 41-62
Rational surfaces over nonclosed fields, 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), 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), Transactions of the AMS 361 (2009), 4471-4489
Weak approximation for hypersurfaces of low degree (with Yuri Tschinkel), 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), American Journal of Mathematics 130 (2008), no. 5, 1263-1278
Log Fano varieties over function fields of curves (with Yuri Tschinkel), Inventiones mathematicae 173 (2008), no. 1, 7-21
Approximation at places of bad reduction for rationally connected varieties (with Yuri Tschinkel), Pure and Applied Mathematics Quarterly 4 (2008), no. 3, 743-766
Weak approximation over function fields (with Yuri Tschinkel), Inventiones mathematicae 163 (2006), 171-190
Classical and minimal models of the moduli space of curves of genus two, 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), Mathematisches Institut, Georg-August-Universität Göttingen: Seminars Summer Term 2004, 135--143, Universitätsdrucke Göttingen, Göttingen, 2004
Universal torsors and Cox rings (with Yuri Tschinkel), 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), Journal of Algebraic Geometry 13 (2004), 233-247
Integral points and effective cones of moduli spaces of stable maps (with Yuri Tschinkel), Duke Mathematical Journal 120 (2003), no. 3, 577-599 Erratum
Potential density of rational points on algebraic varieties, 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, Advances in Mathematics 173, Issue 2, 316-352
On the effective cone of the moduli space of pointed rational curves (with Yuri Tschinkel), 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), Asian Journal of Mathematics 6 (2002), No. 1, 95-100
Density of integral points on algebraic varieties (with Yuri Tschinkel), 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), Geometric and Functional Analysis 11 (2001), no. 6, 1201-1228
Brauer groups and quotient stacks (with Dan Edidin, Andrew Kresch, and Angelo Vistoli), American Journal of Mathematics 123 (2001), no. 4, 761-777
Stable limits of log surfaces and Cohen-Macaulay singularities, Journal of Algebra 242 (2001), no. 1, 225-235
Abelian fibrations and rational points on symmetric products (with Yuri Tschinkel), International Journal of Mathematics 11 (2000), no. 9, 1163-1176
Local stable reduction of plane curve singularities, Journal für die reine und angewandte Mathematik 520 (2000), 169-194
Special cubic fourfolds (abridged version), Compositio Mathematica 120 (2000), no. 1, 1-23
Geometry of equivariant compactifications of Gan (with Yuri Tschinkel), International Mathematical Research Notices 1999, no. 22, 1211-1230
Stable log surfaces and limits of quartic plane curves, manuscripta mathematica 100 (1999), 469-497
Some rational cubic fourfolds, Journal of Algebraic Geometry 8 (1999), 103-114
Correlation for surfaces of general type, Duke Mathematical Journal 85 (1996), no. 1, 95-107
Special cubic fourfolds (longwinded version), revision of Special cubic hypersurfaces of dimension four, Harvard University Thesis (1996)