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

S. Boissiière ; A. Cattaneo ; D. G. Markushevich ; A. Sarti

Izvestiya. Mathematics , Tome 83 (2019) no. 4, pp. 731-742.

Résumé

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-symplectic involution with invariant lattice of rank one. In particular, we describe geometrically some new involutions of the Hilbert square of a K3 surface whose existence was proven in a previous paper of Boissière, Cattaneo, Nieper-Wisskirchen, and Sarti.

Détail

Keywords: irreducible holomorphic symplectic manifolds, non-symplectic automorphisms, ample cone.

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