The geometry of antisymplectic involutions, I

We study fixed loci of antisymplectic involutions on projective hyperkähler manifolds. When the involution is induced by an ample class of square 2 in the BeauvilleBogomolov-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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