O’Grady tenfolds as moduli spaces of sheaves

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...

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Bibliographic Details
Published inForum of mathematics. Sigma Vol. 12
Main Authors Felisetti, Camilla, Giovenzana, Franco, Grossi, Annalisa
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 01.01.2024
Subjects
14E07
14J42
14J50
Automorphisms
Geometry
Investigations
Lattice theory
Sheaves
Topological manifolds
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ISSN2050-5094
2050-5094
DOI10.1017/fms.2024.46

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Summary: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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ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2024.46