Finiteness results for compact hyperkähler manifolds

DOI10.1515/crll.2003.038zbMath1042.53032OpenAlexW1975667994WikidataQ125576865 ScholiaQ125576865MaRDI QIDQ4415684

Daniel Huybrechts

Publication date: 6 August 2003

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crll.2003.038

zbMATH Keywords

complex structureintegral cohomologyPontrjagin classcompact hyper-Kähler manifoldprojectivity criteriondeformation types

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Hyper-Kähler and quaternionic Kähler geometry, ``special geometry (53C26) Complex manifolds (32Q99) Compactification of analytic spaces (32J05)

Related Items (28)

Galois representations on the cohomology of hyper-Kähler varieties ⋮ Positivity of Riemann–Roch polynomials and Todd classes of hyperkähler manifolds ⋮ Absolutely trianalytic tori in the generalized Kummer variety ⋮ Finiteness of Lagrangian fibrations with fixed invariants ⋮ On the Kodaira dimension of orthogonal modular varieties ⋮ Birational boundedness for holomorphic symplectic varieties, Zarhin's trick for \(K3\) surfaces, and the Tate conjecture ⋮ Mapping class group and a global Torelli theorem for hyperkähler manifolds ⋮ Any component of moduli of polarized hyperkähler manifolds is dense in its deformation space ⋮ Computing Riemann–Roch polynomials and classifying hyper-Kähler fourfolds ⋮ Remarks on Kawamata's effective non-vanishing conjecture for manifolds with trivial first Chern classes ⋮ Families of Lagrangian fibrations on hyperkähler manifolds ⋮ Negative Rational Curves and Their Deformations on Hyperkähler Manifolds ⋮ On the Betti numbers of compact holomorphic symplectic orbifolds of dimension four ⋮ Teichmüller space for hyperkähler and symplectic structures ⋮ Twisted cotangent bundle of hyperkähler manifolds (with an appendix by Simone Diverio) ⋮ Hyperbolic geometry of the ample cone of a hyperkähler manifold ⋮ Connected components of moduli spaces of irreducible holomorphic symplectic manifolds of Kummer type ⋮ Morrison-Kawamata cone conjecture for hyperkahler manifolds ⋮ Teichmüller spaces and Torelli theorems for hyperkähler manifolds ⋮ A finiteness theorem for Lagrangian fibrations ⋮ Contraction centers in families of hyperkähler manifolds ⋮ A conjectural bound on the second Betti number for hyper-Kaehler manifolds ⋮ Construction of automorphisms of hyperkähler manifolds ⋮ Holomorphic symplectic geometry: a problem list ⋮ A survey of Torelli and monodromy results for holomorphic-symplectic varieties ⋮ Finiteness of polarized \(K3\) surfaces and hyperkähler manifolds ⋮ A bound on the second Betti number of hyperkähler manifolds of complex dimension six ⋮ Isotriviality of certain Kählerian families of nonprojective manifolds

Cites Work

• Compact hyperkähler manifolds: Basic results
• Unnamed Item

This page was built for publication: Finiteness results for compact hyperkähler manifolds