The geometry of antisymplectic involutions, I

Abstract

We study fixed loci of antisymplectic involutions on projective hyperk\"ahler manifolds. 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.Comment: 45 page