ERC Synergy Grant

Publications by team members

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• Mauro Varesco, The Hodge conjecture for powers of K3 surfaces of Picard number 16, arXiv:2203.09778

• Chenyu Bai, On Abel-Jacobi Maps of Lagrangian Families, arXiv:2203.06242

• Olivier Debarre, Daniel Huybrechts, Emanuele Macrì, Claire Voisin, Computing Riemann-Roch polynomials and classifying hyper-Kähler fourfolds, arXiv:2201.08152

• Claire Voisin, On fibrations and measures of irrationality of hyper-Kähler manifolds, arXiv:2201.07037 

• Arend Bayer, Emanuele Macrì, The unreasonable effectiveness of wall-crossing in algebraic geometry, arXiv:2201.03654

• Georg Oberdieck, Jieao Song, Claire Voisin, Hilbert schemes of K3 surfaces, generalized Kummer, and cobordism classes of hyper-Kähler manifolds, arXiv:2110.02211

• Daniel Huybrechts, Nodal quintic surfaces and lines on cubic fourfolds, arXiv:2108.10532

• Daniel Huybrechts, Mirko Mauri, On type II degenerations of hyperkähler manifolds, arXiv:2108.01587

• Olivier Debarre, Emanuele Macrì, Complete curves in the moduli space of polarized K3 surfaces and hyper-Kähler manifolds, arXiv:2108.00429

• Ignacio Barros, Scott Mullane, On the birational geometry of the moduli of hyperelliptic curves, arXiv:2106.13774

• Claire Voisin,  Footnotes to papers of O'Grady and Markman, arXiv:2106.06979

• Yajnaseni Dutta, Daniel Huybrechts, Maximal variation of curves on K3 surfaces, arXiv:2105.04787

• Alessio Bottini, Stable Sheaves on K3 Surfaces via Wall-Crossing, arXiv:2103.09661

• Laure Flapan, Emanuele Macrì, Kieran O'Grady, Giulia Saccà, The geometry of antisymplectic involutions, I, arXiv:2102.02161

• Olivier Debarre, Giovanni Mongardi, Gushel-Mukai varieties with many symmetries and an explicit irrational Gushel-Mukai threefold, arXiv:2101.01959

• Claire Voisin, Compact Kähler manifolds with no projective specialization, arXiv:2101.01075

• Daniel Huybrechts, Brilliant families of K3 surfaces: Twistor spaces, Brauer groups, and Noether-Lefschetz loci, arXiv:2012.04608

• Daniele Agostini, Ignacio Barros, Kuan-Wen Lai, On the irrationality of moduli spaces of K3 surfaces, arXiv:2011.11025

• Claire Voisin, On the Lefschetz standard conjecture for Lagrangian covered hyper-Kähler varieties, arXiv:2007.11872

• Olivier Debarre, Alexander Kuznetsov, Gushel-Mukai varieties: Intermediate Jacobians, arXiv:2002.05620

• Olivier Debarre, Gushel-Mukai varieties, arXiv:2001.03485

• Arend Bayer, Martí Lahoz, Emanuele Macrì, Howard Nuer, Alexander Perry, Paolo Stellari, Stability conditions in family, arXiv:1902.08184

• Arend Bayer, Martí Lahoz, Emanuele Macrì, Paolo Stellari, Stability conditions on Kuznetsov components, arXiv:1703.10839

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• Lisa Marquand, On Symplectic Birational Involutions of Manifolds of OG10 type, arXiv:2206.13814

• Valery Alexeev, Root systems and hyperkahler varieties, arXiv:2206.14070 

• Luca Giovenzana, Annalisa Grossi, Claudio Onorati, Davide Cesare Veniani, Symplectic rigidity of O'Grady's tenfolds, arXiv:2206.11594 

• Adam Czapliński, Andreas Krug, Manfred Lehn, Sönke Rollenske, Compactified Jacobians of Extended ADE Curves and Lagrangian Fibrations, arXiv:2206.11686 

• Kazuhiro Ito, Tetsushi Ito, Teruhisa Koshikawa, The Hodge standard conjecture for self-products of K3 surfaces, arXiv:2206.10086 

• Georg Oberdieck, Lagrangian planes in hyperkähler varieties of K3[n]-type, arXiv:2206.10288 

• Valeria Bertini, Annalisa Grossi, Rational curves on primitive symplectic varieties of OG6 singular type, arXiv:2206.00691

• Brendan Hassett, Yuri Tschinkel, Equivariant derived equivalence and rational points on K3 surfaces, arXiv:2205.14470

• Francesco Denisi, The pseudo-effective cone of the known irreducible holomorphic symplectic manifolds, arXiv:2205.15148

• Ekaterina Amerik, Frédéric Campana, On algebraically coisotropic submanifolds of holomorphic symplectic manifolds, arXiv:2205.07958

• Soheyla Feyzbakhsh, Hyperkähler varieties as Brill-Noether loci on curves, arXiv:2205.00681

• Bert van Geemen, Fourfolds of Weil type and the spinor map, arXiv:2205.00483

• Chen Jiang, Positivity of Riemann-Roch polynomials and Todd classes of hyperkähler manifolds, arXiv:2008.04685

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• Kieran O'Grady, Theta groups and projective models of hyperkähler varieties, arXiv:2204.09582

• Francesco Meazzini, Claudio Onorati, Hyper-holomorphic connections on vector bundles on hyper-Kähler manifolds, arXiv:2204.04075

• Eyal Markman, Rational Hodge isometries of hyper-Kahler varieties of K3[n]-type are algebraic, arXiv:2204.00516

• Salvatore Floccari, On the motive of O'Grady's six dimensional hyper-Kähler varieties, arXiv:2203.16257

• Hanfei Guo, Zhiyu Liu, Shizhuo Zhang, A moduli theoretic approach to Lagrangian subvarieties of hyperkähler varieties: Examples, arXiv:2203.13091

• Valeria Bertini, Franco Giovenzana, Hodge structure of O'Grady's singular moduli spaces, arXiv:2203.07917

• Kieran O'Grady, Modular sheaves on hyperkähler fourfolds of Kummer type, arXiv:2203.03987

• Franco Giovenzana, Luca Giovenzana, Claudio Onorati, On the period of Li, Pertusi and Zhao's symplectic variety, arXiv:2202.13702

• Thorsten Beckmann, Atomic Objects on hyper-Kähler manifolds, arXiv:2202.01184

• Junliang Shen, Qizheng Yin, Perverse-Hodge complexes for Lagrangian fibrations, arXiv:2201.11283

• René Mboro, Basic remarks on Lagrangian submanifolds of Hyper-Kähler manifolds, arXiv:2201.06135

• Simone Novario, Geometric description of ⟨2⟩-polarised Hilbert squares of generic K3 surfaces, arXiv:2201.05074

• Laura Pertusi, Paolo Stellari, Categorical Torelli theorems: results and open problems, arXiv:2201.03899

• Lie Fu, Zhiyuan Li, Haitao Zou, Unpolarized Shafarevich conjectures for hyper-Kähler varieties, arXiv:2201.03350

• Zhiyuan Li, Xun Zhang, Deligne-Beilinson cohomology of the universal K3 surface, arXiv:2201.02367 

• Zhiyuan Li, Xun Zhang, Beauville-Voisin filtrations on zero cycles of moduli space of stable sheaves on K3 surfaces, arXiv:2201.00493

• Justin Sawon, Topological bounds on hyperkähler manifolds, arXiv:2112.11617

• Anna Abasheva, Vasily Rogov, Shafarevich-Tate groups of holomorphic Lagrangian fibrations, arXiv:2112.10921

• Lie Fu, Robert Laterveer, Special cubic fourfolds, K3 surfaces and the Franchetta property, arXiv:2112.02437

• Elham Izadi, Samir Canning, Yajnaseni Dutta, David Stapleton, Hyperkähler manifolds, arXiv:2112.02435

• Ekaterina Amerik, Misha Verbitsky, Parabolic automorphisms of hyperkahler manifolds, arXiv:2112.01951

• Marcello Bernardara, Enrico Fatighenti, Laurent Manivel, Fabio Tanturri, Fano fourfolds of K3 type, arXiv:2111.13030

• Haidong Liu, On the existence of rational curves on projective hyperkähler fourfolds, arXiv:2111.04270

• Michael Hoff, Giovanni Staglianò, Explicit constructions of K3 surfaces and unirational Noether-Lefschetz divisors, arXiv:2110.15819

• Valery Alexeev, Philip Engel, The flex divisor of a K3 surface, arXiv:2109.14603

• Kohei Kikuta, Spherical twists and the center of autoequivalence groups of K3 surfaces, arXiv:2110.14353

• Yoon-Joo Kim, The dual Lagrangian fibration of known hyper-Kähler manifolds, arXiv:2109.03987

• Eunjeong Lee, Kyeong-Dong Park, Complete intersection hyperkähler fourfolds with respect to equivariant vector bundles over rational homogeneous varieties of Picard number one, arXiv:2108.13314 

• Camilla Felisetti, Junliang Shen, Qizheng Yin, On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties, arXiv:2108.02464 

• Teppei Takamatsu, On the finiteness of twists of hyperkähler varieties, arXiv:2106.11651

• Vladimiro Benedetti, Jieao Song, Divisors in the moduli space of Debarre-Voisin varieties, arXiv:2106.06859

• Francesco Denisi, Boucksom-Zariski and Weyl chambers on irreducible holomorphic symplectic manifolds, arXiv:2106.03678

• Ben Wu, Hodge Numbers of O'Grady 6 Via Ngô Strings, arXiv:2105.08545

• Grzegorz Kapustka, Bert van Geemen, Contractions of hyper-Kähler fourfolds and the Brauer group, arXiv:2105.07697

• Christian Lehn, Giovanni Mongardi, Gianluca Pacienza, Deformations of rational curves on primitive symplectic varieties and applications, arXiv:2103.13522

• Volodymyr Gavran, Tangent bundle of a manifold of K3[2]-type is rigid, arXiv:2103.13522

• Thorsten Beckmann, Derived categories of hyper-Kähler manifolds: extended Mukai vector and integral structure, arXiv:2103.13382

• Emilio Franco, Degeneration of natural Lagrangians and Prymian integrable systems, arXiv:2103.05553

• Justin Sawon, Chen Shen, Deformations of compact Prym fibrations to Hitchin systems, arXiv:2103.04274

• Georg Oberdieck, Gromov-Witten theory and Noether-Lefschetz theory for holomorphic-symplectic varieties, arXiv:2102.11622

• Francesco Viganò, Complex Multiplication and Noether-Lefschetz Loci of the Twistor Space of a K3 Surface, arXiv:2102.07285

• Renat Abugaliev, Characteristic foliation on hypersurfaces with positive Beauville-Bogomolov-Fujiki square, arXiv:2102.02799

• Jieao Song, On the image of the period map for polarized hyperkähler manifolds of K3[m]-type, arXiv:2101.04791

• Valeria Bertini, Rational curves on O'Grady's tenfolds, arXiv:2101.01029

• Arvid Perego, Antonio Rapagnetta, The second integral cohomology of moduli spaces of sheaves on K3 and Abelian surfaces, arXiv:2012.10649

• Dominique Mattei, A Lagrangian fibration on a moduli space of sheaves on a K3 surface, arXiv:2012.05848

• Arnaud Beauville, A remark on the generalized Franchetta conjecture for K3 surfaces, arXiv:2012.03332

• Andreas Kretschmer, The Chow ring of hyperkähler varieties of K3[2]-type via Lefschetz actions, arXiv:2010.13847

• Giovanni Mongardi, Claudio Onorati, Birational geometry of irreducible holomorphic symplectic tenfolds of O'Grady type, arXiv:2010.12511 

• Grégoire Menet, Ulrike Rieß, On the Kähler cone of irreducible symplectic orbifolds, arXiv:2009.04873

• Annalisa Grossi, Claudio Onorati, Davide Veniani, Prime order symplectic birational transformations of O'Grady's holomorphic symplectic sixfolds, arXiv:2009.02120 

• Chen Jiang, Positivity of Riemann-Roch polynomials and Todd classes of hyperkähler manifolds, arXiv:2008.04685

• Chunyi Li, Laura Pertusi, Xiaolei Zhao, Elliptic quintics on cubic fourfolds, O'Grady 10, and Lagrangian fibrations, arXiv:2007.14108

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• Hanine Awada, Michele Bolognesi, Claudio Pedrini, A family of special cubic fourfolds with motive of abelian type, arXiv:2007.07193

• Thorsten Beckmann, Georg Oberdieck, Equivariant categories and fixed loci of holomorphic symplectic varieties arXiv:2006.13899

• Ángel David Ríos Ortiz, Riemann-Roch Polynomials of the known Hyperkähler Manifolds, arXiv:2006.09307

• Giulia Saccà, Birational geometry of the intermediate Jacobian fibration of a cubic fourfold, arXiv:2002.01420

• Kieran O’Grady, Modular sheaves on hyperkähler varieties, arXiv:1912.02659

• Eduard Looijenga, Teichmüller spaces and Torelli theorems for hyperkähler manifolds, arXiv:1912.02550