Modern Aspects of Geometry: Categories, Cycles and Cohomology of Hyperkähler Varieties

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Publications

The geometry of cubic hypersurfaces

Author(s): Daniel Huybrechts
Published in: Cambridge Stud. Adv. Math.,, 2023
Publisher: CUP

Stability conditions in families

Author(s): Bayer, Arend; Lahoz, Martí; Macrì, Emanuele; Nuer, Howard; Perry, Alexander; Stellari, Paolo
Published in: Publications Mathématiques. Institut de Hautes Études Scientifiques, 2021, ISSN 0073-8301
Publisher: Springer Verlag
DOI: 10.1007/s10240-021-00124-6

On automorphic forms of small weight for fake projective planes

Author(s): Galkin, Sergey; Karzhemanov, Ilya; Shinder, Evgeny
Published in: Mosc. Math. J., 2023, ISSN 1609-3321
Publisher: Independent University of Moscow

Characteristic foliations — A survey

Author(s): Fabrizio Anella, Daniel Huybrechts
Published in: Bulletin of the London Mathematical Society, Issue 56, 2024, Page(s) 2231-2249, ISSN 0024-6093
Publisher: Oxford University Press
DOI: 10.1112/blms.13107

Kernels of categorical resolutions of nodal singularities

Author(s): Warren Cattani, Franco Giovenzana, Shengxuan Liu, Pablo Magni, Luigi Martinelli, Laura Pertusi, Jieao Song
Published in: Rendiconti del Circolo Matematico di Palermo Series 2, Issue 72, 2023, Page(s) 3077-3105, ISSN 0009-725X
Publisher: Circolo Matematico di Palermo
DOI: 10.1007/s12215-023-00895-3

Schiffer variations and the generic Torelli theorem for hypersurfaces

Author(s): Claire Voisin
Published in: Compositio Math., 2022, ISSN 0010-437X
Publisher: London Mathematical Society
DOI: 10.1112/s0010437x21007727

On fibrations and measures of irrationality of hyper-Kähler manifolds

Author(s): Claire Voisin
Published in: Rev. Un. Mat. Argentina, Issue 00416932, 2022, ISSN 0041-6932
Publisher: Union Matematica Argentina
DOI: 10.33044/revuma.3319

On the Hodge and Betti numbers of hyper-Kähler manifolds

Author(s): Pietro Beri and Olivier Debarre
Published in: Milan Journal of Mathematics, 2021, ISSN 1424-9286
Publisher: Birkhauser Verlag
DOI: 10.1007/s00032-022-00367-w

Chow groups of surfaces of lines in cubic fourfolds

Author(s): Daniel Huybrechts
Published in: Épijournal de géométrie algébrique, 2023, ISSN 2491-6765
Publisher: Association de l'Épijournal de géométrie algébrique
DOI: 10.46298/epiga.2023.10425

Effectivity of semi-positive line bundles

Author(s): Fabrizio Anella, Daniel Huybrechts
Published in: Milan Journal of Mathematics, 2022, ISSN 1424-9286
Publisher: Birkhauser Verlag
DOI: 10.1007/s00032-022-00356-z

Groups Acting on Moduli Spaces of Hyper-Kähler Manifolds

Author(s): Francesca Rizzo
Published in: Milan Journal of Mathematics, Issue 92, 2024, Page(s) 169-193, ISSN 1424-9286
Publisher: Birkhauser Verlag
DOI: 10.1007/s00032-024-00396-7

Compact Kähler manifolds with no projective specialization

Author(s): Claire Voisin
Published in: Bollettino dell'Unione Matematica Italiana, Springer Verlag, 2021, Issue 2, 2022, ISSN 1972-6724
Publisher: Unione Matematica Italiana
DOI: 10.1007/s40574-021-00288-3

Gushel–Mukai varieties with many symmetries and an explicit irrational Gushel–Mukai threefold

Author(s): Olivier Debarre; Giovanni Mongardi
Published in: Boll. Unione Mat. Ital., Issue 5, 2022, ISSN 1972-6724
Publisher: Unione Matematica Italiana
DOI: 10.1007/s40574-021-00293-6

On the Lefschetz standard conjecture for Lagrangian covered hyper-Kähler varieties

Author(s): Claire Voisin
Published in: Advances in Mathematics, 2022, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2021.108108

Hilbert schemes of K3 surfaces, generalized Kummer, and cobordism classes of hyper-Kähler manifolds

Author(s): Georg Oberdieck, Jieao Song, Claire Voisin
Published in: Pure and Applied Mathematics Quarterly, 2022, ISSN 1558-8599
Publisher: International Press

Footnotes to papers of O’Grady and Markman

Author(s): Claire Voisin
Published in: Mathematische Zeitschrift, 2022, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-021-02883-8

Computing Riemann-Roch polynomials and classifying hyper-Kähler fourfold

Author(s): Olivier Debarre, Daniel Huybrechts, Emanuele Macri, Claire Voisin
Published in: Journal of the American Mathematical Society, Issue 08940347, 2022, ISSN 0894-0347
Publisher: American Mathematical Society
DOI: 10.1090/jams/1016

Smooth subvarieties of Jacobians

Author(s): Olivier Benoist; Olivier Debarre
Published in: Épijournal de géométrie algébrique., Issue 3, 2023, ISSN 2491-6765
Publisher: Association de l'Épijournal de géométrie algébrique
DOI: 10.46298/epiga.2023.10321

Gushel-Mukai varieties: intermediate Jacobians

Author(s): Debarre, Olivier; Kuznetsov, Alexander
Published in: Épijournal Géom, 2020, ISSN 2491-6765
Publisher: Association de l'Épijournal de géométrie algébrique

The cotangent bundle of K3 surfaces of degree two

Author(s): Fabrizio Anella, Andreas Höring
Published in: Épijournal de Géométrie Algébrique, Issue Special volume in honour of..., 2023, ISSN 2491-6765
Publisher: SMF
DOI: 10.46298/epiga.2023.9960

Complex multiplication in twistor spaces

Author(s): Daniel Huybrechts
Published in: Int. Math. Res. Not. IMRN, 2021, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnaa073

Lagrangian fibrations

Author(s): Daniel Huybrechts, Mirko Mauri
Published in: Milan Journal Math., 2022, ISSN 1424-9286
Publisher: Birkhauser Verlag
DOI: 10.1007/s00032-022-00349-y

Author(s): Mauro Varesco
Published in: Mathematische Zeitschrift, Issue 305, 2023, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-023-03390-8

Maximal variation of curves on K3 surfaces

Author(s): Yajnaseni Dutta, Daniel Huybrechts
Published in: Tunisian Journal of Mathematics, 2022, ISSN 2576-7658
Publisher: Math. Sci. Publ.
DOI: 10.2140/tunis.2022.4.443

On Abel-Jacobi Maps of Lagrangian Families

Author(s): Chenyu Bai
Published in: Mathematische Zeitschrift, 2023, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-023-03292-9

On the irrationality of moduli spaces of K3 surfaces

Author(s): Daniele Agostini; Ignacio Barros; Kuan-Wen Lai
Published in: Trans. Amer. Math. Soc, Issue 1, 2023, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/8830

Rational curves on primitive symplectic varieties of OG$$_6^s$$-type

Author(s): Valeria Bertini, Annalisa Grossi
Published in: Mathematische Zeitschrift, Issue 304, 2023, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-023-03296-5

A categorical Torelli theorem for hypersurfaces

Author(s): Dmitrii Pirozhkov
Published in: Bulletin of the London Mathematical Society, Issue 56, 2024, Page(s) 3075-3089, ISSN 0024-6093
Publisher: Oxford University Press
DOI: 10.1112/blms.13117

Hyper-Kähler manifolds of generalized Kummer type and the Kuga–Satake correspondence

Author(s): Claire Voisin, Mauro Varesco
Published in: Milan Journal of Mathematics, 2022, ISSN 1424-9286
Publisher: Birkhauser Verlag
DOI: 10.1007/s00032-022-00369-8

On fibrations and measures of irrationality of hyper-Kähler manifolds

Author(s): Claire Voisin
Published in: Rev. Un. Mat. Argentina, Issue 9, 2023, ISSN 1669-9637
Publisher: Unión Matemática Argentina

Stably semiorthogonally indecomposable varieties

Author(s): Dmitrii Pirozhkov
Published in: Épijournal de Géométrie Algébrique, Issue Volume 7, 2023, ISSN 2491-6765
Publisher: Paris
DOI: 10.46298/epiga.2023.volume7.7700

The geometry of antisymplectic involutions, I.

Author(s): Emanuele Macri
Published in: Mathematische Zeitschrift, 2022, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-021-02909-1

Hyper-Kähler manifolds of generalized Kummer type and the Kuga–Satake correspondence

Author(s): Claire Voisin, Mauro Varesco
Published in: Milan Journal of Mathematics, Issue 1, 2023, ISSN 1424-9286
Publisher: Birkhauser Verlag

Stability and applications

Author(s): Emanuele Macri, Benjamin Schmidt
Published in: Pure and Applied Mathematics Quarterly, 2022, ISSN 1558-8599
Publisher: International Press
DOI: 10.4310/pamq.2021.v17.n2.a5

On birational transformations of Hilbert schemes of points on K3 surfaces

Author(s): Beri, Pietro; Cattaneo, Alberto
Published in: Mathematische Zeitschrift, 2022, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-021-02960-y

On type II degenerations of hyperkähler manifolds

Author(s): Daniel Huybrechts, Mirko Mauri
Published in: Mathematical Research Letters, 2022, ISSN 1073-2780
Publisher: Mathematical Publishing
DOI: 10.4310/mrl.2023.v30.n1.a6

Lagrangian fibrations of hyperkähler fourfolds

Author(s): Daniel Huybrechts, Chenyang Xu
Published in: Journal of the Institute of Mathematics of Jussieu. JIMJ, 2022, ISSN 1474-7480
Publisher: Cambridge University Press
DOI: 10.1017/s1474748020000365

The Looijenga–Lunts–Verbitsky Algebra and Verbitsky’s Theorem

Author(s): Alessio Bottini
Published in: Milan Journal of Mathematics, Issue 1, 2023, ISSN 1424-9286
Publisher: Birkhauser Verlag
DOI: 10.1007/s00032-022-00364-z

On the coniveau of rationally connected threefolds

Author(s): Claire Voisin
Published in: Geometry and Topology, 2022, ISSN 1465-3060
Publisher: University of Warwick
DOI: 10.2140/gt.2022.26.2731

Nodal quintic surfaces and lines on cubic fourfolds (with an appendix by John Christian Ottem)

Author(s): Daniel Huybrechts
Published in: L’Enseignement Mathématique, Issue 70, 2024, Page(s) 499-532, ISSN 0013-8584
Publisher: EMS Press
DOI: 10.4171/lem/1063

Rouquier dimension of some blow-ups

Author(s): Dmitrii Pirozhkov
Published in: European Journal of Mathematics volume, 2023, ISSN 2199-675X
Publisher: Springer
DOI: 10.1007/s40879-023-00639-8

Brilliant families of K3 surfaces: Twistor spaces, Brauer groups, and Noether-Lefschetz loci

Author(s): Huybrechts, Daniel
Published in: Annals de la Faculte des Sciences de Toulouse, Issue 1, 2022, ISSN 2258-7519
Publisher: Centre Mersenne, Annales de la Faculté des Sciences de Toulouse, et les auteurs

Derived Categories of Hyper-Kähler Manifolds via the LLV Algebra

Author(s): T. Beckmann
Published in: Milan Journal of Mathematics, Issue 9, 2022, ISSN 1424-9286
Publisher: Birkhauser Verlag
DOI: 10.1007/s00032-022-00358-x

New rational cubic fourfolds arising from Cremona transformations

Author(s): Yu-Wei Fan, Kuan-Wen Lai
Published in: Algebraic Geometry, 2023, ISSN 2313-1691
Publisher: Foundation Compositio Mathematics
DOI: 10.14231/ag-2023-014

Homological Bondal-Orlov localization conjecture for rational singularities

Author(s): Mirko Mauri, Evgeny Shinder
Published in: Forum of Mathematics, Sigma, 2022, ISSN 2050-5094
Publisher: Cambridge Univ. Press
DOI: 10.1017/fms.2023.65

Nielsen realization problem for derived automorphisms of generic K3 surfaces

Author(s): Fan, Yu-Wei; Lai, Kuan-Wen
Published in: Issue 1, 2023
Publisher: submitted
DOI: 10.48550/arxiv.2302.12663

"Kodaira dimension of moduli spaces of hyperk\""ahler varieties"

Author(s): Barros, Ignacio; Beri, Pietro; Brakkee, Emma; Flapan, Laure
Published in: Issue 4, 2022
Publisher: submitted

Remarks on the Bondal quiver

Author(s): Sung, Benjamin
Published in: Issue 1, 2022
Publisher: arxiv
DOI: 10.48550/arxiv.2210.08638

Fourier-Mukai numbers of K3 categories of very general special cubic fourfolds

Author(s): Fan, Yu-Wei; Lai, Kuan-Wen
Published in: Issue 1, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2307.14486

Polygons of Newton-Okounkov type on irreducible holomorphic symplectic manifolds

Author(s): Denisi, Francesco Antonio
Published in: Issue 1, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2311.03295

The Hodge conjecture for powers of K3 surfaces of Picard number 16

Author(s): Mauro Varesco
Published in: 2022
Publisher: submitted

The K3 category of a cubic fourfold -- an update

Author(s): Daniel Huybrechts
Published in: Issue 6, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2303.03820

Stability conditions on non-commutative curves

Author(s): Sung, Benjamin
Published in: Issue 1, 2022
Publisher: arxiv
DOI: 10.48550/arxiv.2210.08637

The special Brauer group and twisted Picard varieties

Author(s): Daniel Huybrechts, Dominique Mattei
Published in: 2023
Publisher: arxiv

Derived equivalence of elliptic K3 surfaces and Jacobians

Author(s): Reinder Meinsma, Evgeny Shinder
Published in: 2023
Publisher: submitted

On the irrationality of moduli spaces of projective hyperkähler manifolds

Author(s): Daniele Agostini, Ignacio Barros, Kuan-Wen Lai
Published in: 2023
Publisher: submitted

Special subvarieties in the locus of intermediate Jacobians of cubic

Author(s): Moritz Hartlieb
Published in: 2023
Publisher: submitted

Towards a modular construction of OG10

Author(s): Alessio Bottini
Published in: 2022
Publisher: submitted

Categorical Torelli theorem for hypersurfaces

Author(s): Dmitrii Pirozhkov
Published in: 2022
Publisher: submitted

Crossing the transcendental divide: from Schottky groups to algebraic curves

Author(s): Fairchild, Samantha; Ortiz, Ángel David Ríos
Published in: Issue 5, 2024
Publisher: arxiv
DOI: 10.48550/arxiv.2401.10801

The Kodaira classification of the moduli of hyperelliptic curves

Author(s): Barros, Ignacio; Mullane, Scott
Published in: Issue 5, 2021
Publisher: arxiv
DOI: 10.48550/arxiv.2106.13774

On the transcendental lattices of Hyperkähler manifolds

Author(s): Benedetta Piroddi, Ángel David Ríos Ortiz
Published in: 2023
Publisher: submitted

The Intermediate Jacobian fibration of a cubic fourfold containing a plane and fibrations in Prym varieties

Author(s): Mattei, Dominique
Published in: Issue 2, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2302.00350

Terminalizations of quotients of compact hyperkähler manifolds by induced symplectic automorphisms

Author(s): Bertini, Valeria; Grossi, Annalisa; Mauri, Mirko; Mazzon, Enrica
Published in: Issue 5, 2024
Publisher: arxiv
DOI: 10.48550/arxiv.2401.13632

Complete curves in the moduli space of polarized K3 surfaces and hyper-K��hler manifolds

Author(s): Debarre, Olivier; Macrì, Emanuele
Published in: Issue 1, 2021
Publisher: arxiv
DOI: 10.48550/arxiv.2108.00429

On symplectic birational self-maps of projective hyperkähler manifolds of K3[n]-type

Author(s): Yajnaseni Dutta, Dominique Mattei, Yulieth Prieto-Montañez
Published in: 2022
Publisher: submitted

Cycle classes on abelian varieties and the geometry of the Abel-Jacobi map

Author(s): Claire Voisin
Published in: 2022
Publisher: submitted

EPW sextics associated to K3 surfaces

Author(s): Pietro Beri
Published in: Issue 5, 2020
Publisher: arxiv
DOI: 10.48550/arxiv.2011.12223

Symmetric tensors on the intersection of two quadrics and Lagrangian fibration

Author(s): A. Beauville, A. Etesse, A. Höring, J. Liu, C. Voisin
Published in: Issue 14, 2023
Publisher: arxiv

Flat pushforwards of Chern classes and the smoothability of cycles in the Whitney range

Author(s): Kollár, János; Voisin, Claire
Published in: Issue 3, 2023
Publisher: arxiv

The unreasonable effectiveness of wall-crossing in algebraic geometry

Author(s): Bayer, Arend; Macr��, Emanuele
Published in: Issue 22, 2022
Publisher: arxiv
DOI: 10.48550/arxiv.2201.03654

Stable Sheaves on K3 Surfaces via Wall-Crossing

Author(s): Bottini, Alessio
Published in: submitted, 2021
Publisher: under review

Algebraic cycles on hyper-Kähler varieties of generalized Kummer type

Author(s): Salvatore Floccari, Mauro Varesco
Published in: 2023
Publisher: submitted

Towards generic base point freeness for generalized Kummer varieties in low dimension

Author(s): Mauro Varesco
Published in: 2021
Publisher: submitted

The geometry of antisymplectic involutions, II

Author(s): Laure Flapan, Emanuele Macrì, Kieran G. O'Grady, Giulia Saccà
Published in: 2023
Publisher: submitted

Homologically finite-dimensional objects in triangulated categories

Author(s): Alexander Kuznetsov, Evgeny Shinder,
Published in: Issue 5, 2022
Publisher: arxiv
DOI: 10.48550/arxiv.2211.09418

Geometric representability of 1-cycles on rationally connected threefolds

Author(s): Claire Voisin
Published in: 2022
Publisher: submitted

Complete curves in the moduli space of polarized K3 surfaces and hyper-Kähler manifolds

Author(s): Olivier Debarre, Emanuele Macri
Published in: submitted, 2021
Publisher: under review

On some birational invariants of hyper-Kähler manifolds

Author(s): Chenyu Bai
Published in: 2022
Publisher: submitted

On Chern classes of Lagrangian fibered hyper-Kähler manifolds

Author(s): Claire Voisin
Published in: Issue 5, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2305.09396

Splitting unramified Brauer classes by abelian torsors and the period-index problem

Author(s): Daniel Huybrechts, Dominique Mattei
Published in: 2023
Publisher: arxiv

Mukai bundles on Fano threefolds

Author(s): Bayer, Arend; Kuznetsov, Alexander; Macrì, Emanuele
Published in: Issue 5, 2024
Publisher: arxiv
DOI: 10.48550/arxiv.2402.07154

Special subvarieties in the locus of intermediate Jacobians of cubic threefolds

Author(s): Hartlieb, Moritz
Published in: Issue 1, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2304.03214

A birational involution

Author(s): Pietro Berri and Laurent Manivel
Published in: 2022
Publisher: submitted

Geometric representability of 1-cycles on rationally connected threefolds

Author(s): Voisin, Claire
Published in: 2022, Issue 4, 2022
Publisher: arxiv
DOI: 10.48550/arxiv.2208.12557

Functorial constructions related to double Poisson vertex algebras

Author(s): Bozec, Tristan; Fairon, Maxime; Moreau, Anne
Published in: 2023, Issue 4, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2307.06071

On maximally non-factorial nodal Fano threefolds

Author(s): Ivan Cheltsov, Igor Krylov, Jesus Martinez Garcia, Evgeny Shinder
Published in: 2023
Publisher: submitted

Gushel-Mukai varieties

Author(s): Olivier Debarre
Published in: 2020
Publisher: under review

Isotrivial Lagrangian fibrations of compact hyper-Kähler manifolds

Author(s): Kim, Yoon-Joo; Laza, Radu; Martin, Olivier
Published in: Issue 5, 2023
Publisher: arxiv
DOI: 10.48550/arxiv.2312.15147

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