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arXiv · 2102.02161

The geometry of antisymplectic involutions, I

Laure Flapan·Emanuele Macrì·Kieran G. O'Grady·Giulia Saccà
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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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Laure Flapan, Emanuele Macrì, Kieran G. O'Grady, Giulia Saccà. 2021-02-03. The geometry of antisymplectic involutions, I. https://doi.org/10.1007/s00209-021-02909-1

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