Forum of Mathematics, Sigma (Jan 2024)

O’Grady tenfolds as moduli spaces of sheaves

  • Camilla Felisetti,
  • Franco Giovenzana,
  • Annalisa Grossi

DOI
https://doi.org/10.1017/fms.2024.46
Journal volume & issue
Vol. 12

Abstract

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We give a lattice-theoretic characterization for a manifold of $\operatorname {\mathrm {OG10}}$ type to be birational to some moduli space of (twisted) sheaves on a K3 surface. We apply it to the Li–Pertusi–Zhao variety of $\operatorname {\mathrm {OG10}}$ type associated to any smooth cubic fourfold. Moreover, we determine when a birational transformation is induced by an automorphism of the K3 surface, and we use this to classify all induced birational symplectic involutions.

Keywords