Kyoto Journal of Mathematics

Moduli spaces of bundles over nonprojective K3 surfaces

Arvid Perego and Matei Toma

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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.

Article information

Kyoto J. Math., Volume 57, Number 1 (2017), 107-146.

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

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Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 32G13: Analytic moduli problems {For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10} [See also 14H15, 14J15] 53C26: Hyper-Kähler and quaternionic Kähler geometry, "special" geometry

moduli spaces of sheaves twisted sheaves K3 surfaces


Perego, Arvid; Toma, Matei. Moduli spaces of bundles over nonprojective K3 surfaces. Kyoto J. Math. 57 (2017), no. 1, 107--146. doi:10.1215/21562261-3759540.

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