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Towards a modular construction of OG10

Part of: Surfaces and higher-dimensional varieties Symplectic geometry, contact geometry

Published online by Cambridge University Press:  08 November 2024

Alessio Bottini
Alessio Bottini*
Affiliation:
Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy [email protected] Université Paris-Saclay, CNRS, Laboratoire de Mathématiques d'Orsay, Rue Michel Magat, Bât. 307, 91405 Orsay, France
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Abstract

We construct the first example of a stable hyperholomorphic vector bundle of rank five on every hyper-Kähler manifold of $\mathrm {K3}^{[2]}$-type whose deformation space is smooth of dimension 10. Its moduli space is birational to a hyper-Kähler manifold of type OG10. This provides evidence for the expectation that moduli spaces of sheaves on a hyper-Kähler could lead to new examples of hyper-Kähler manifolds.

Keywords

Hyper-Kähler manifoldsstable vector bundlesmoduli spaces

MSC classification

Primary: 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli 53D30: Symplectic structures of moduli spaces
Type
Research Article
Information
Compositio Mathematica , Volume 160 , Issue 10 , October 2024 , pp. 2496 - 2529
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Copyright
© The Author(s), 2024. The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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Footnotes

Current address: Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany

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