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.

46 pages. v2: Minor corrections, references updated

References in corpus (2)

• Mapping class group and global Torelli theorem for hyperkahler manifolds: an erratum
• Stability and Applications

Cited by in corpus (1)

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