The geometry of antisymplectic involutions, I

Abstract

We study fixed loci of antisymplectic involutions on projective hyperkähler manifolds of ${K3}^{[n]}$-type. When the involution is induced by an ample class of square 2 in the Beauville-Bogomolov-Fujiki lattice, we show that the number of connected components of the fixed locus is equal to the divisibility of the class, which is either 1 or 2.

arXiv comment46 pages. v2: Minor corrections, references updated

References in corpus (10)

• A survey of Torelli and monodromy results for holomorphic-symplectic varieties
• Markov convexity and local rigidity of distorted metrics
• Mapping class group and global Torelli theorem for hyperkahler manifolds: an erratum
• MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations
• Antisymplectic involutions of holomorphic symplectic manifolds
• Integral constraints on the monodromy group of the hyperkahler resolution of a symmetric product of a K3 surface
• Prime exceptional divisors on holomorphic symplectic varieties and monodromy-reflections
• Derived automorphism groups of K3 surfaces of Picard rank 1
• Küchle fivefolds of type c5
• Stability and Applications

Cited by in corpus (1)

• Equivariant geometry of odd-dimensional complete intersections of two quadrics