Aleksandr Kuznetsov

Publications⁸⁴

• Article A. G. Kuznetsov, Yu. G. Prokhorov. On higher-dimensional del Pezzo varieties // Izvestiya. Mathematics. 2023. Vol. 87. No. 3. P. 75-148. doi
• Article Kuznetsov A., Prokhorov Y. Rationality of Fano threefolds over non-closed fields // American Journal of Mathematics. 2023. Vol. 145. No. 2. P. 335-411. doi
• Article Shinder E., Kuznetsov A., Karmazyn J. Derived categories of singular surfaces // Journal of the European Mathematical Society. 2022. Vol. 24. No. 2. P. 461-526. doi
• Preprint Kuznetsov A., Shinder E. Homologically finite-dimensional objects in triangulated categories / Cornell University. Series arXiv "math". 2022.
• Preprint Prokhorov Y., Kuznetsov A. On higher-dimensional del Pezzo varieties / Cornell University. Series arXiv "math". 2022.
• Article Kuznetsov A., Prokhorov Y. Rationality over nonclosed fields of Fano threefolds with higher geometric Picard rank // Journal of the Institute of Mathematics of Jussieu. 2022. P. 1-41. doi
• Article Kuznetsov A. Simultaneous categorical resolutions // Mathematische Zeitschrift. 2022. Vol. 300. P. 3551-3576. doi
• Article Kuznetsov A. Derived Categories of Families of Sextic del Pezzo Surfaces // International Mathematics Research Notices. 2021. Vol. 2021. No. 12. P. 9262-9339. doi
• Article Belmans P., Kuznetsov A., Smirnov M. Derived categories of the Cayley plane and the coadjoint Grassmannian of type F // Transformation Groups. 2021 doi
• Article Kuznetsov A., Perry A. Homological projective duality for quadrics // Algebraic Geometry. 2021. Vol. 30. P. 457-476. doi
• Preprint Kuznetsov A. Quadric bundles and hyperbolic equivalence / Cornell University. Series arXiv "math". 2021.
• Preprint Prokhorov Y., Kuznetsov A. Rationality over non-closed fields of Fano threefolds with higher geometric Picard rank / Cornell University. Series arXiv "math". 2021.
• Preprint Kuznetsov A., Perry A. Serre functors and dimensions of residual categories / Cornell University. Series arXiv "math". 2021.
• Preprint Kuznetsov A. Simultaneous categorical resolutions / Cornell University. Series arXiv "math". 2021.
• Article Cheltsov I., Kuznetsov A., Shramov K. Coble fourfold, 𝔖6-invariant quartic threefolds, and Wiman–Edge sextics // Algebra & Number Theory. 2020. Vol. 14. No. 1. P. 213-274. doi
• Preprint Kuznetsov A., Smirnov M., Belmans P. Derived categories of the Cayley plane and the coadjoint Grassmannian of type F / Cornell University. Series arXiv "math". 2020.
• Preprint Kuznetsov A., Debarre O. Gushel--Mukai varieties: intermediate Jacobians / Cornell University. Series arXiv "math". 2020.
• Article Kuznetsov A., Smirnov M. On residual categories for Grassmannians // Proceedings of the London Mathematical Society. 2020. Vol. 120. No. 5. P. 617-641. doi
• Preprint Prokhorov Y., Kuznetsov A. Rationality of Mukai varieties over non-closed fields / Cornell University. Series arXiv "math". 2020.
• Preprint Kuznetsov A., Smirnov M. Residual categories for (co)adjoint Grassmannians in classical types / Cornell University. Series arXiv "math". 2020.
• Article Kuznetsov A. Calabi–Yau and fractional Calabi–Yau categories // Journal fuer die reine und angewandte Mathematik. 2019. Vol. 2019. No. 753. P. 239-267. doi
• Preprint Perry A., Kuznetsov A. Categorical cones and quadratic homological projective duality / Cornell University. Series arXiv "math". 2019.
• Article Kuznetsov A., Debarre O. Gushel–Mukai varieties: Linear spaces and periods // Kyoto Journal of Mathematics. 2019. Vol. 4. No. 59. P. 897-953. doi
• Preprint Kuznetsov A., Perry A. Homological projective duality for quadrics / Cornell University. Series arXiv "math". 2019.
• Article Cruz Morales J. A., Mellit A., Kuznetsov A., Smirnov M., Perrin N. On quantum cohomology of Grassmannians of isotropic lines, unfoldings of An-singularities, and Lefschetz exceptional collections // Annales de l'Institut Fourier. 2019. Vol. 69. No. 3. P. 955-991. doi
• Preprint Kuznetsov A., Prokhorov Y. Rationality of Fano threefolds over non-closed fields / Cornell University. Series arXiv "math". 2019.
• Article Кузнецов А. Г. Вложение производных категорий поверхностей Энриквеса в производные категории многообразий Фано // Известия РАН. Серия математическая. 2019. Т. 83. № 3. С. 127-132. doi
• Preprint Kuznetsov A., Perry A. Categorical joins / Cornell University. Series arXiv "math". 2018.
• Preprint Cheltsov I., Kuznetsov A., Shramov K. Coble fourfold, S_6-invariant quartic threefolds, and Wiman-Edge sextics / Cornell University. Series math "arxiv.org". 2018.
• Article Fonarev A., Kuznetsov A. Derived Categories of Curves as Components of Fano Manifolds // Journal of London Mathematical Society. 2018. Vol. 97. No. 2. P. 24-46. doi
• Article Kuznetsov A., Perry A. Derived categories of Gushel-Mukai varieties // Compositio Mathematica. 2018. Vol. 154. No. 7. P. 1362-1406. doi
• Preprint Kuznetsov A., Shinder E., Karmazyn J. Derived categories of singular surfaces / Cornell University. Series arXiv "math". 2018.
• Article Kuznetsov A. Derived equivalence of Ito-Miura-Okawa-Ueda Calabi-Yau 3-folds // Journal of the Mathematical Society of Japan. 2018. Vol. 70. No. 3. P. 1007-1013. doi
• Preprint Kuznetsov A., Debarre O. Double covers of quadratic degeneracy and Lagrangian intersection loci / Cornell University. Series arXiv "math". 2018.
• Preprint Kuznetsov A. Embedding derived categories of Enriques surfaces into derived categories of Fano varieties / Cornell University. Series arXiv "math". 2018.
• Article Kuznetsov A., Shinder E. Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics // Selecta Mathematica, New Series. 2018. Vol. 24. No. 4. P. 3475-3500. doi
• Article Kuznetsov A., Debarre O. Gushel-Mukai varieties: Classification and birationalities // Algebraic Geometry. 2018. Vol. 5. No. 1. P. 15-76. doi
• Preprint Kuznetsov A., Debarre O. Gushel-Mukai varieties: moduli / Cornell University. Series arXiv "math". 2018.
• Article Prokhorov Y., Kuznetsov A., Shramov K. Hilbert schemes of lines and conics and automorphism groups of Fano threefolds // Japanese Journal of Mathematics. 2018. Vol. 13. No. 1. P. 109-185.
• Article Kuznetsov A. On linear sections of the spinor tenfold. I // Izvestiya: Mathematics. 2018. Vol. 82. No. 4. P. 694-751. doi
• Preprint Kuznetsov A., Smirnov M. On residual categories for Grassmannians / Cornell University. Series arXiv "math". 2018.
• Article Kuznetsov A., Prokhorov Y. Prime Fano threefolds of genus 12 with a Gm-action and their automorphisms // Épijournal de Géométrie Algébrique. 2018. Vol. 2. No. 3. P. 1-14.
• Article Michael Finkelberg, Alexander Kuznetsov, Leonid Rybnikov, Dobrovolska G. Towards a cluster structure on trigonometric zastava // Selecta Mathematica, New Series. 2018. Vol. 24. No. 1. P. 187-225. doi
• Article Kuznetsov A. Calabi-Yau and fractional Calabi-Yau categories // Journal fuer die reine und angewandte Mathematik. 2017 doi (in press)
• Article Alexander Kuznetsov, Perry A. Derived categories of cyclic covers and their branch divisors // Selecta Mathematica, New Series. 2017. Vol. 23. No. 1. P. 389-423. doi
• Preprint Prokhorov Y., Kuznetsov A. Prime Fano threefolds of genus 12 with a G_m-action / Cornell University. Series arXiv "math". 2017.
• Chapter Kuznetsov A. Derived Categories View on Rationality Problems, in: Rationality Problems in Algebraic Geometry Levico Terme, Italy 2015 Vol. 2172. Switzerland : Springer, 2016. P. 67-104. doi
• Preprint Kuznetsov A., Perry A. Derived categories of Gushel-Mukai varieties / Cornell University. Series arXiv "math". 2016.
• Preprint Fonarev A., Kuznetsov A. Derived categories of curves as components of Fano manifolds / Cornell University. Series arXiv "math". 2016.
• Preprint Kuznetsov A. Derived equivalence of Ito-Miura-Okawa-Ueda Calabi-Yau 3-folds / Cornell University. Series arXiv "math". 2016.
• Article Kuznetsov A., Polishchuk A. Exceptional collections on isotropic Grassmannians // Journal of the European Mathematical Society. 2016. Vol. 18. No. 3. P. 507-574.
• Preprint Kuznetsov A., Shinder E. Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics / Cornell University. Series arXiv "math". 2016.
• Preprint Debarre O., Kuznetsov A. Gushel-Mukai varieties: linear spaces and periods / Cornell University. Series arXiv "math". 2016.
• Preprint Kuznetsov A., Prokhorov Y., Shramov K. Hilbert schemes of lines and conics and automorphism groups of Fano threefolds / Cornell University. Series arXiv "math". 2016.
• Article Finkelberg M. V., Ginzburg V., Ionov A., Kuznetsov A. Intersection cohomology of the Uhlenbeck compactification of the Calogero-Moser space // Selecta Mathematica, New Series. 2016. Vol. 22. No. 4. P. 2491-2534. doi
• Preprint Kuznetsov A., Debarre O. On the cohomology of Gushel-Mukai sixfolds / Cornell University. Series arXiv "math". 2016.
• 
  Book Beauville A., Hassett B., Kuznetsov A., Verra A. Rationality Problems in Algebraic Geometry Levico Terme, Italy 2015 Vol. 2172. Switzerland : Springer, 2016.
• Article Finkelberg M. V., Kuznetsov A., Rybnikov L., Dobrovolska G. Towards a cluster structure on trigonometric zastava // Selecta Mathematica, New Series. 2016 doi (in press)
• Article Michael Finkelberg, Leonid Rybnikov, Alexander Kuznetsov, Dobrovolska G. Towards a cluster structure on trigonometric zastava // Selecta Mathematica, New Series. 2016. P. 1-39. doi (in press)
• Preprint Kuznetsov A. Calabi-Yau and fractional Calabi-Yau categories / Cornell University. Series math "arxiv.org". 2015.
• Article Kuznetsov A., Lunts V. Categorical Resolutions of Irrational Singularities // International Mathematics Research Notices. 2015. No. 13 doi
• Preprint Kuznetsov A. Derived categories view on rationality problems / Cornell University. Series math "arxiv.org". 2015.
• Preprint Kuznetsov A., Debarre O. Gushel--Mukai varieties: classification and birationalities / Cornell University. Series math "arxiv.org". 2015.
• Article Kuznetsov A. Height of exceptional collections and Hochschild cohomology of quasiphantom categories // Journal fuer die reine und angewandte Mathematik. 2015. Vol. 2015. No. 708. P. 213-243. doi
• Preprint Finkelberg M. V., Ginzburg V., Ionov A., Kuznetsov A. Intersection cohomology of the Uhlenbeck compactification of the Calogero-Moser space / Cornell University. Series math "arxiv.org". 2015.
• Preprint Alexander Kuznetsov. On Küchle manifolds with Picard number greater than 1 / Cornell University. Series math "arxiv.org". 2015.
• Article Ingalls C., Kuznetsov A. On nodal Enriques surfaces and quartic double solids // Mathematische Annalen. 2015. Vol. 361. No. 1-2. P. 107-133. doi
• Article Kaledin D., Kuznetsov A. Refined blowups // Mathematical Research Letters. 2015. Vol. 22. No. 6. P. 1717-1732. doi
• Preprint Finkelberg M. V., Kuznetsov A., Rybnikov L. G., Dobrovolska G. Towards a cluster structure on trigonometric zastava / Cornell University. Series math "arxiv.org". 2015.
• Article А.Г.Кузнецов О многообразиях Кюхле с числом Пикара, большим 1 // Известия РАН. Серия математическая. 2015. Т. 79. № 4. С. 3-16. (in press)
• Preprint Alexander Kuznetsov, Perry A. Derived categories of cyclic covers and their branch divisors / Cornell University. Series math "arxiv.org". 2014.
• Preprint D. Kaledin, A. Kuznetsov. Refined blowups / Cornell University. Series math "arxiv.org". 2014.
• Article A. Kuznetsov. Scheme of lines on a family of 2-dimensional quadrics: geometry and derived category // Mathematische Zeitschrift. 2014. Vol. 276. No. 3. P. 655-672. doi
• Preprint Alexander Kuznetsov. Semiorthogonal decompositions in algebraic geometry / Cornell University. Series math "arxiv.org". 2014.
• Preprint Kuznetsov A. A simple counterexample to the Jordan-Hölder property for derived categories / Cornell University. Series math "arxiv.org". 2013.
• Preprint Kuznetsov A., Lunts V. Categorical resolutions of irrational singularities / Cornell University. Series math "arxiv.org". 2012. No. 1212.6170 .
• Preprint Kuznetsov A. Height of exceptional collections and Hochschild cohomology of quasiphantom categories / Cornell University. Series math "arxiv.org". 2012. No. 1211.4693.
• Article Kuznetsov A. Instanton bundles on Fano threefolds // Central European Journal of Mathematics. 2012. Vol. 10. No. 4. P. 1198-1231. doi
• Article Kuznetsov A. Base change for semiorthogonal decompositions // Compositio Mathematica. 2011. Vol. 147. P. 852-876.
• Preprint Kuznetsov A., Polishchuk A. Exceptional collections on isotropic Grassmannians / Cornell University. Series math "arxiv.org". 2011. No. 1110.5607 .
• Article Kuznetsov A. Abel-Jacobi maps for hypersurfaces and non commutative Calabi-Yau's // Communications in Contemporary Mathematics. 2010. Vol. 12. No. 3. P. 373-416.
• Chapter Alexander Kuznetsov. Derived Categories of Cubic Fourfolds, in: Cohomological and Geometric Approaches to Rationality Problems / Сост.: Fedor Bogomolov, Y. Tschinkel. Boston : Birkhäuser, 2010. P. 219-243.
• Preprint Kuznetsov A., Ingalls C. On nodal Enriques surfaces and quartic double solids / Cornell University. Series math "arxiv.org". 2010. No. 1012.3530.
• Preprint Kuznetsov A. Scheme of lines on a family of 2-dimensional quadrics: geometry and derived category / Cornell University. Series math "arxiv.org". 2010. No. 1011.4146.