On the existence of universal families of marked irreducible holomorphic symplectic manifolds

Abstract

We prove the existence of a universal family over every component of the moduli space of marked irreducible holomorphic symplectic manifolds. The analogous result follows for the Teichmuller spaces.

v2: 13 pages, accepted for publication in Kyoto J. of Math

References in corpus (4)

• Mapping class group and global Torelli theorem for hyperkahler manifolds: an erratum
• Introduction to the language of stacks and gerbes
• The global moduli theory of symplectic varieties
• The Noether-Lefschetz conjecture and generalizations

Cited by in corpus (8)

• Mapping class group and global Torelli theorem for hyperkahler manifolds: an erratum
• Contraction centers in families of hyperkahler manifolds
• Rational Hodge isometries of hyper-Kahler varieties of K3[n]-type are algebraic
• Holomorphic anomaly equations for the Hilbert scheme of points of a K3 surface
• MBM loci in families of hyperkahler manifolds and centers of birational contractions
• Kodaira dimension of universal holomorphic symplectic varieties
• Rigid hyperholomorphic sheaves remain rigid along twistor deformations of the underlying hyparkahler manifold
• Tautological families of cyclic covers of projective spaces