The geometry of antisymplectic involutions, I

摘要

We study fixed loci of antisymplectic involutions on projective hyperkahler 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.