Publications and preprints of Alexander Kuznetsov

Lists of publications at MathSciNet, MathNet, Arxiv, Google Scholar.

Authors Title Reference
[75] A. Kuznetsov Simultaneous categorical resolutions preprint math.AG/2101.06943
[74] A. Kuznetsov, Yu. Prokhorov Rationality of Mukai varieties over non-closed fields preprint math.AG/2003.10761
[73] A. Kuznetsov, Yu. Prokhorov Rationality of Fano threefolds over non-closed fields preprint math.AG/1911.08949
[72] A. Kuznetsov, A. Perry Categorical cones and quadratic homological projective duality preprint math.AG/1902.09824
[71] A. Kuznetsov, M. Smirnov Residual categories for (co)adjoint Grassmannians in classical types preprint math.AG/2001.04148, to appear in Compositio Mathematica
[70] P. Belmans, A. Kuznetsov, M. Smirnov Derived categories of the Cayley plane and the coadjoint Grassmannian of type F preprint math.AG/2005.01989, to appear in Transformation Groups
[69] A. Kuznetsov, A. Perry Categorical joins preprint math.AG/1804.00144, to appear in JAMS
[68] J. Karmazyn, A. Kuznetsov, E. Shinder Derived categories of singular surfaces preprint math.AG/1809.10628, to appear in JEMS
[67] A. Kuznetsov, A. Perry Homological projective duality for quadrics preprint math.AG/1902.09832, to appear in JAG (published online)
[66] A. Kuznetsov Derived categories of families of sextic del Pezzo surfaces to appear in IMRN (published online)
[65] O. Debarre, A. Kuznetsov Gushel-Mukai varieties: intermediate Jacobians EpiGA, epiga:6475 (2020), Volume 4
[64] O. Debarre, A. Kuznetsov Double covers of quadratic degeneracy and Lagrangian intersection loci Math. Annalen 378 (2020), no. 3, 1435-1469
[63] O. Debarre, A. Kuznetsov Gushel-Mukai varieties: moduli Int. Journal of Math. 31 (2020), no. 2, 2050013
[62] I. Cheltsov, A. Kuznetsov, C. Shramov Coble fourfold, S6-invariant quartic threefolds, and Wiman--Edge sextics Algebra Number Theory 14 (2020), no. 1, 213-274
[61] A. Kuznetsov, M. Smirnov On residual categories for Grassmannians Proc. London Math. Soc. 120 (2020), 617-641.
[60] O. Debarre, A. Kuznetsov Gushel-Mukai varieties: linear spaces and periods Kyoto Journal of Math. Volume 59, Number 4 (2019), 897-953.
[59] A. Kuznetsov Calabi-Yau and fractional Calabi-Yau categories J. Reine Angew. Math. 753 (2019), 239--267.
[58] A. Kuznetsov Embedding derived categories of Enriques surfaces in derived categories of Fano varieties Izvestiya: Mathematics (2019), 83 (3):534--539
[57] J.A. Cruz Morales, A. Kuznetsov, A. Mellit, N. Perrin, M. Smirnov On quantum cohomology of Grassmannians of isotropic lines, unfoldings of An-singularities, and Lefschetz exceptional collections Annales de l'Institut Fourier, Volume 69 (2019) no. 3, p. 955--991
[56] A. Kuznetsov On linear sections of the spinor tenfold, I Izvestiya: Mathematics 82:4 (2018) pp. 694--751
[55] A. Kuznetsov, E. Shinder Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics Selecta Math, V. 24 (2018), No. 4, pp. 3475--3500
[54] A. Kuznetsov, Yu. Prokhorov Prime Fano threefolds of genus 12 with a Gm-action Épijournal de Géométrie Algébrique, V. 2 (2018), Article 3
[53] A. Kuznetsov Derived equivalence of Ito-Miura-Okawa-Ueda Calabi-Yau 3-folds JMSJ, V. 70 (2018), No. 3, pp. 1007--1013
[52] A. Kuznetsov, A. Perry Derived categories of Gushel-Mukai varieties Compositio Mathematica, V. 154 (2018), N. 7, pp. 1362--1406
[51] A. Kuznetsov, Yu. Prokhorov, C. Shramov Hilbert schemes of lines and conics and automorphism groups of Fano threefolds Japanese Journal of Mathematics, V. 13 (2018), N. 1, pp. 109-185
[50] M. Finkelberg, A. Kuznetsov, L. Rybnikov, G. Dobrovolska Towards a cluster structure on trigonometric zastava Selecta Math, V. 24 (2018), N. 1, pp. 187-225.
[49] A. Fonarev, A. Kuznetsov Derived categories of curves as components of Fano manifolds Journal of the LMS, V. 97 (2018), N. 1, pp. 24-46.
[48] O. Debarre, A. Kuznetsov Gushel-Mukai varieties: classification and birationalities Algebraic Geometry, V. 5 (2018), N. 1, pp. 15--76.
[47] A. Kuznetsov Exceptional collections in surface-like categories Sbornik: Mathematics, V. 208 (2017), N. 9, pp. 1368--1398.
[46] A. Kuznetsov, A. Perry Derived categories of cyclic covers and their branch divisors Selecta Math, V. 23 (2017), N. 1, pp. 389--423
[45] A. Kuznetsov Derived categories view on rationality problems "Rationality Problems in Algebraic Geometry: Levico Terme, Italy 2015", Pardini, Rita and Pirola, Gian Pietro (Eds.) 2016, ISBN: 978-3-319-46209-7 Springer International Publishing
[44] O. Debarre, A. Kuznetsov On the cohomology of Gushel-Mukai sixfolds preprint math.AG/1606.09384
[43] A. Kuznetsov Küchle fivefolds of type c5 Math. Zeitschrift, V. 284 (2016), N. 3, pp 1245--1278
[42] M. Finkelberg, V. Ginzburg, A. Ionov, A. Kuznetsov Intersection cohomology of the Uhlenbeck compactification of the Calogero-Moser space Selecta Math., V. 22 (2016), N. 4, pp 2491-2534
[41] A. Kuznetsov, A. Polishchuk Exceptional collections on isotropic Grassmannians J. Eur. Math. Soc. (JEMS) 18 (2016), no. 3, 507--574
[40] A. Kuznetsov On Küchle manifolds with Picard number greater than 1 Izvestiya RAN: Ser. Mat. 79:4 (2015) p. 57-70 (in Russian); translation in Izvestiya: Mathematics 79:4 (2015) p. 698-709
[39] D. Kaledin, A. Kuznetsov Refined blowups Mathematical Research Letters, Volume 22, Number 6, 1717–1732, 2015
[38] A. Kuznetsov, V. Lunts Categorical resolutions of irrational singularities International Mathematical Research Notices 2015, No. 13, p. 4536-4625
[37] A. Kuznetsov Height of exceptional collections and Hochschild cohomology of quasiphantom categories J. Reine Angew. Math. 708 (2015), 213--243
[36] C. Ingalls, A. Kuznetsov On nodal Enriques surfaces and quartic double solids Mathematische Annalen, Volume 361, Issue 1--2 (2015), pp 107--133.
[35] A. Kuznetsov Semiorthogonal decompositions in algebraic geometry preprint math.AG/1404.3143, Proceedings of ICM-2014
[34] A. Kuznetsov Scheme of lines on a family of 2-dimensional quadrics: geometry and derived category Math. Zeitschrift, Volume 276, Issue 3 (2014), Page 655-672.
[33] A. Kuznetsov A simple counterexample to the Jordan-Hölder property for derived categories preprint math.AG/1304.0903
[32] A. Kuznetsov Instanton bundles on Fano threefolds CEJM 2012, 10(4), 1198-1231
[31] A. Kuznetsov Base change for semiorthogonal decompositions Compositio Mathematica / Volume 147 / Issue 03, (2011) pp 852 - 876, preprint math.AG/0711.1734
[30] A. Kuznetsov Derived categories of cubic fourfolds "Cohomological and Geometric Approaches to Rationality Problems. New Perspectives" Series: Progress in Mathematics, Vol. 282, Bogomolov, Fedor; Tschinkel, Yuri (Eds.) 2010, X, 314 p. 47 illus., Hardcover ISBN: 978-0-8176-4933-3 A Birkhauser book
[29] A. Kuznetsov, L. Manivel and D. Markushevich Abel-Jacobi maps for hypersurfaces and non commutative Calabi-Yau's Communications in Contemporary Mathematics Vol. 12, No. 3 (2010) 373-416
[28] A. Kuznetsov Hochschild homology and semiorthogonal decompositions preprint math.AG/0904.4330
[27] A. Kuznetsov Derived categories of Fano threefolds Proc. V.A.Steklov Inst. Math, V. 264 (2009), p. 110-122
[26] A. Kuznetsov and D. Markushevich Symplectic structures on moduli spaces of sheaves via the Atiyah class Journal of Geometry and Physics, V. 59 (2009) N. 7, 843-860
[25] A. Kuznetsov Homological projective duality for Grassmannians of lines preprint math.AG/0610957
[24] A. Kuznetsov Lefschetz decompositions and categorical resolutions of singularities Selecta Mathematica, V. 13 (2008), N. 4, 661-696
[23] A. Kuznetsov Exceptional collections for Grassmannians of isotropic lines Proceedings of the London Mathematical Society, V. 97 (2008), N. 1, 155-182
[22] A. Kuznetsov Derived categories of quadric fibrations and intersections of quadrics Advances in Mathematics, V. 218 (2008), N. 5, 1340-1369
[21] A. Kuznetsov Homological projective duality Publications Mathematiques de L'IHES, 105, n. 1 (2007), 157-220
[20] A. Kuznetsov Quiver varieties and Hilbert schemes Moscow Mathematical Journal, Volume 7 (2007), Number 4
[19] A. Kuznetsov Hyperplane sections and derived categories Izvestiya RAN: Ser. Mat. 70:3 (2006) p. 23-128 (in Russian); translation in Izvestiya: Mathematics 70:3 (2006) p. 447-547.
[18] A. Kuznetsov Derived categories of Fano threefolds V12 Mat. zametki, V. 78, n. 4 (2005), p. 579-594, translation in Mathematical Notes, V. 78, n. 4 (2005), p. 537-550
[17] A. Kuznetsov Derived categories of cubic and V14 threefolds Proc. V.A.Steklov Inst. Math, V. 246 (2004), p. 183-207
[16] V. Baranovsky, V. Ginzburg and A. Kuznetsov Wilson's grassmanian and a noncommutative quadric International Mathematical Research Notices, 2003, No. 21, p. 1155-1197
[15] M. Finkelberg, D. Gaitsgory, A. Kuznetsov Uhlenbeck spaces for A2 and affine Lie algebra \hat{sl}_n Publ. Res. Inst. Math. Sci., V. 39 (2003), No. 4, p. 721-766
[14] V. Baranovsky, V. Ginzburg and A. Kuznetsov Quiver varieties and a noncommutative P2 Compositio Mathematica, 2002, V. 134, p. 283-318
[13] A. Kapustin, A. Kuznetsov and D. Orlov Noncommutative instantons and twistor transform Communications in Mathematical Physics, 2001, No. 220, p. 385-432
[12] M. Finkelberg and A. Kuznetsov Parabolic sheaves on surfaces and affine Lie algebra \hat{gl}_n J. reine angew. Math., 2000, V. 529, p. 155-203
[11'] Erratum to: A note on a simplectic structure on the space of G-monopoles Communications in Mathematical Physics, 2015, Volume 334, Issue 2, pp 1153-1155
[11] M. Finkelberg, A. Kuznetsov, N. Markarian and I. Mirkovic A note on a simplectic structure on the space of G-monopoles Communications in Mathematical Physics, 1999, No. 201, p. 411-421
[10] B. Feigin, M. Finkelberg, A. Kuznetsov and I. Mirkovic Semi-Infinite flags II. Local and global intersection cohomology of quasimaps' spaces Differential topology, infinite-dimensional Lie algebras, and applications, p. 113-148, Amer. Math. Soc. Transl. Ser. 2, 194, Amer. Math. Soc., Providence, RI, 1999
[9] M. Finkelberg, A. Kuznetsov and I. Mirkovic The singular supports of IC sheaves on quasimaps' spaces are irreducible American Mathematical Society Translations, Series 2, 1998, V. 185, p. 85-93
[8] A. Kuznetsov Fano threefolds V22 preprint MPIM/97-24
[7] A. Kuznetsov The length 2 monad for instantons over P3 with c2 = 3 preprint MPIM/97-22
[6] A. Kuznetsov GL4-equivariant desingularization of the universal curve over the Ellingsrud-Piene-Stromme compactiffcation of the space of twisted rational cubic curves in P3 preprint MPIM/97-21
[5] M. Finkelberg and A. Kuznetsov Global intersection cohomology of quasimaps' spaces International Mathematical Research Notices, 1997, No. 7, p. 301-328
[4] A. Kuznetsov The Laumon's resolution of Drinfeld's compactification is small Mathematical Research Letters, 1997, V. 4, p. 349-364.
[3] A. Kuznetsov An exceptional collection of vector bundles on V22 Fano threefolds Vestnik MGU, Ser. 1, Mat. Mekh. 1996, no. 3, p. 41-44 (in Russian)
[2] A. Kuznetsov, I. Pak and A. Postnikov Trees associated with Motzkin numbers J. Combin. Theory Ser. A, 1996, V. 76, no. 1, p. 145-147
[1] A. Kuznetsov, I. Pak and A. Postnikov Increasing trees and alternating permutations Uspehi Matem. Nauk, 1994, V. 49, no. 6, p. 79-110