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April 2017 Moduli spaces of bundles over nonprojective K3 surfaces
Arvid Perego, Matei Toma
Kyoto J. Math. 57(1): 107-146 (April 2017). DOI: 10.1215/21562261-3759540

Abstract

We study moduli spaces of sheaves over nonprojective K3 surfaces. More precisely, let ω be a Kähler class on a K3 surface S, let r2 be an integer, and let v=(r,ξ,a) be a Mukai vector on S. We show that if the moduli space M of μω-stable vector bundles with associated Mukai vector v is compact, then M is an irreducible holomorphic symplectic manifold which is deformation equivalent to a Hilbert scheme of points on a K3 surface. Moreover, we show that there is a Hodge isometry between v and H2(M,Z) and that M is projective if and only if S is projective.

Citation

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Arvid Perego. Matei Toma. "Moduli spaces of bundles over nonprojective K3 surfaces." Kyoto J. Math. 57 (1) 107 - 146, April 2017. https://doi.org/10.1215/21562261-3759540

Information

Received: 8 December 2014; Revised: 2 October 2015; Accepted: 20 January 2016; Published: April 2017
First available in Project Euclid: 11 March 2017

zbMATH: 1362.14010
MathSciNet: MR3621782
Digital Object Identifier: 10.1215/21562261-3759540

Subjects:
Primary: 14D20, 32G13, 53C26

Rights: Copyright © 2017 Kyoto University

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Vol.57 • No. 1 • April 2017
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