Characterizing projective spaces on deformations of Hilbert schemes of K3 surfaces

DOI10.1002/cpa.20384zbMath1235.14037arXiv1011.1285OpenAlexW2963016522MaRDI QIDQ3112617

David I. Harvey, Yuri Tschinkel, Brendan Hassett

Publication date: 11 January 2012

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.1285

zbMATH Keywords

irreducible symplectic manifolds

Mathematics Subject Classification ID

(K3) surfaces and Enriques surfaces (14J28) (n)-folds ((n>4)) (14J40)

Related Items

Character formulas on cohomology of deformations of Hilbert schemes ofK3 surfaces ⋮ Moduli spaces of sheaves on \(K3\) surfaces ⋮ A CLASSIFICATION OF LAGRANGIAN PLANES IN HOLOMORPHIC SYMPLECTIC VARIETIES ⋮ On \(k\)-gonal loci in Severi varieties on general \(K3\) surfaces and rational curves on hyperkähler manifolds ⋮ MMP for moduli of sheaves on \(K3\)s via wall-crossing: nef and movable cones, Lagrangian fibrations ⋮ Lagrangian 4-planes in holomorphic symplectic varieties of \(K3^{[4}\)-type] ⋮ Tautological classes on moduli spaces of hyper-Kähler manifolds ⋮ Rational curves in holomorphic symplectic varieties and Gromov-Witten invariants

Uses Software

• Magma
• SageMath
• mwrank

Cites Work

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• Hodge cycles, motives, and Shimura varieties
• Heisenberg algebra and Hilbert schemes of points on projective surfaces
• The Magma algebra system. I: The user language
• The cup product of Hilbert schemes for K3 surfaces
• Cohomology of compact hyperkähler manifolds and its applications
• Moving and ample cones of holomorphic symplectic fourfolds
• Generators of the cohomology ring of moduli spaces of sheaves on symplectic surfaces
• Moduli spaces of irreducible symplectic manifolds
• Hodge theory and Lagrangian planes on generalized Kummer fourfolds
• On the monodromy of moduli spaces of sheaves on K3 surfaces
• Rational curves on holomorphic symplectic fourfolds.