## Kyoto Journal of Mathematics

### Moduli spaces of bundles over nonprojective K3 surfaces

#### Abstract

We study moduli spaces of sheaves over nonprojective K3 surfaces. More precisely, let $\omega$ be a Kähler class on a K3 surface $S$, let $r\geq2$ be an integer, and let $v=(r,\xi,a)$ be a Mukai vector on $S$. We show that if the moduli space $M$ of $\mu_{\omega}$-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 $v^{\perp}$ and $H^{2}(M,\mathbb{Z})$ and that $M$ is projective if and only if $S$ is projective.

#### Article information

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

Dates
Revised: 2 October 2015
Accepted: 20 January 2016
First available in Project Euclid: 11 March 2017

https://projecteuclid.org/euclid.kjm/1489201233

Digital Object Identifier
doi:10.1215/21562261-3759540

Mathematical Reviews number (MathSciNet)
MR3621782

Zentralblatt MATH identifier
1362.14010

#### Citation

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. https://projecteuclid.org/euclid.kjm/1489201233

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