| Authors | Title | Reference | |
|---|---|---|---|
| [88] | A. Bayer, A. Kuznetsov, E. Macrì | Mukai bundles on Fano threefolds | preprint math.AG/2402.07154 |
| [87] | A. Kuznetsov, Yu. Prokhorov | One-nodal Fano threefolds with Picard number one | preprint math.AG/2312.13782 |
| [86] | A. Kuznetsov, E. Shinder | Derived categories of Fano threefolds and degenerations | preprint math.AG/2305.17213 |
| [85] | A. Kuznetsov, E. Shinder | Homologically finite-dimensional objects in triangulated categories | preprint math.AG/2211.09418 |
| [84] | A. Kuznetsov | Derived categories of families of Fano threefolds | preprint math.AG/2202.12345 |
| [83] | A. Kuznetsov, A. Perry | Serre functors and dimensions of residual categories | preprint math.AG/2109.02026 |
| [82] | A. Kuznetsov | Quadric bundles and hyperbolic equivalence | preprint math.AG/2108.01546, to appear in Geometry & Topology |
| [81] | J.-L. Colliot-Thélène, A. Kuznetsov | Retour sur l’arithmétique des intersections de deux quadriques | J. Reine Angew. Math. (published online) |
| [80] | A. Kuznetsov, Yu. Prokhorov | Rationality over non-closed fields of Fano threefolds with higher geometric Picard rank | JIMJ, Volume 23 (2024) Issue 1, 207-247 |
| [79] | A. Kuznetsov, E. Shinder | Categorical absorptions of singularities and degenerations | EPIGA, Volume spécial en l'honneur de Claire Voisin, 2024 |
| [78] | A. Kuznetsov | Explicit deformation of the horospherical variety of type G2 | Math. Sb., 214:8, 1111-1120 (2023) |
| [77] | A. Kuznetsov, Yu. Prokhorov | On higher-dimensional del Pezzo varieties | Izv. RAN. Ser. Mat., 87:3, 488-561 (2023) |
| [76] | A. Kuznetsov, Yu. Prokhorov | Rationality of Fano threefolds over non-closed fields | AJM 145, No. 2, 335-411 (2023) |
| [75] | A. Kuznetsov, A. Perry | Categorical cones and quadratic homological projective duality | ASENS (4) 56 (2023), no. 1, 1-57 |
| [74] | P. Belmans, A. Kuznetsov, M. Smirnov | Derived categories of the Cayley plane and the coadjoint Grassmannian of type F | Transformation Groups 28 (2023), pp. 9-34 |
| [73] | A. Kuznetsov | Semiorthogonal decompositions in families | preprint math.AG/2111.00527, Proceedings of ICM-2022 |
| [72] | A. Kuznetsov | Simultaneous categorical resolutions | Math. Zeitschrift 300 (2022), pp. 3551-3576 |
| [71] | J. Karmazyn, A. Kuznetsov, E. Shinder | Derived categories of singular surfaces | JEMS 24 (2022), no. 2, pp. 461-526 |
| [70] | A. Kuznetsov, Yu. Prokhorov | Rationality of Mukai varieties over non-closed fields | "Rationality of Varieties", Series: Progress in Mathematics, Vol. 342, Farkas, G; van der Geer, G.; Shen, M; Taelman, L (Eds.) 2021. |
| [69] | A. Kuznetsov, M. Smirnov | Residual categories for (co)adjoint Grassmannians in classical types | Compositio Mathematica, 157 (2021), no. 6, 1172-1206 |
| [68] | A. Kuznetsov, A. Perry | Homological projective duality for quadrics | JAG 30 (2021), p. 457-476 |
| [67] | A. Kuznetsov | Derived categories of families of sextic del Pezzo surfaces | IMRN (2021), no. 12, p. 9262-9339 |
| [66] | A. Kuznetsov, A. Perry | Categorical joins | JAMS 34 (2021), 505-564 |
| [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 |