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arXiv · 2303.07017

O'Grady tenfolds as moduli spaces of sheaves

Camilla Felisetti·Franco Giovenzana·Annalisa Grossi
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Abstract

We give a lattice-theoretic characterization for a manifold of $\mathrm{OG}10$ 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 $\mathrm{OG}10$ 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.

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Camilla Felisetti, Franco Giovenzana, Annalisa Grossi. 2023-03-13. O'Grady tenfolds as moduli spaces of sheaves. https://arxiv.org/abs/2303.07017

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