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The geometry of antisymplectic involutions, I
Published 3 Feb 2021 in math.AG | (2102.02161v2)
Abstract: We study fixed loci of antisymplectic involutions on projective hyperk\"ahler manifolds of $\mathrm{K3}{[n]}$-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.
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