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.
O’Grady tenfolds as moduli spaces of sheaves / Felisetti, Camilla; Giovenzana, Franco; Grossi, Annalisa. - In: FORUM OF MATHEMATICS. SIGMA. - ISSN 2050-5094. - 12:(2024), pp. 1-20. [10.1017/fms.2024.46]
O’Grady tenfolds as moduli spaces of sheaves
Felisetti, Camilla
;
2024
Abstract
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.
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