On the nonsymplectic involutions of the Hilbert square of a K3 surface

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Abstract

We investigate the interplay between the moduli spaces of ample $\langle 2\rangle$-polarized IHS manifolds of type $\mathrm{K3}^{[2]}$and of IHS manifolds of type $\mathrm{K3}^{[2]}$ with a non-symplecticinvolution with invariant lattice of rank one. In particular, wedescribe geometrically some new involutions of the Hilbert square of a K3 surface whose existence was proven in a previous paper ofBoissière, Cattaneo, Nieper-Wisskirchen, and Sarti.

About the authors

Samuel Boissière

Université de Poitiers

Email: samuel.boissiere@math.univ-poitiers.fr

Andrea Cattaneo

Institut Camille Jordan, Université Claude Bernard Lyon 1

Email: cattaneo@math.univ-lyon1.fr

Dmitri Genrikhovich Markushevich

Université de Lille

Alessandra Sarti

Université de Poitiers

Email: sarti@math.univ-poitiers.fr

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