O'Grady tenfolds as moduli spaces of sheaves

2023/03/13 by Camilla Felisetti, Felisetti, Camilla, Franco Giovenzana +3 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2303.07017

Abstract

We give a lattice-theoretic characterization for a manifold of 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 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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• Some remarks on L-equivalence for cubic fourfolds and hyper-Kähler manifolds

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