Irreducibility of moduli spaces of vector bundles on K3 surfaces

Abstract

In this paper, we show the moduli spaces of stable sheaves on K3 surfaces are irreducible symplectic manifolds, if the associated Mukai vectors are primitive. More precisely, we show that they are related to the Hilbert scheme of points. We also compute the period of these spaces. As an application of our result, we discuss Montonen-Olive duality in Physics. In particular our computations of Euler characteristics of moduli spaces are compatible with Physical computations by Minahan et al.

arXiv comment21 pages, one section is added

References in corpus (4)

• Theta functions and Hodge numbers of moduli spaces of sheaves on rational surfaces
• The weight-two Hodge structure of moduli spaces of sheaves on a K3 surface
• Euler characteristics of SU(2) instanton moduli spaces on rational elliptic surfaces
• Equivalences of triangulated categories and Fourier-Mukai transforms

Cited by in corpus (21)

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• On the monodromy of moduli spaces of sheaves on K3 surfaces II
• Twisted stability and Fourier-Mukai transform
• Moduli spaces of stable sheaves on Enriques surfaces
• {\cal N}=4 Supersymmetric Yang-Mills Theory on Orbifold-$T^4/{\mathbf{Z}}_2$: Higher Rank Case
• Derived and abelian equivalence of K3 surfaces
• An Approach to $\mathcal{N}=4$ ADE Gauge Theory on K3
• The second integral cohomology of moduli spaces of sheaves on K3 and Abelian surfaces
• Moduli spaces of stable sheaves on abelian surfaces
• A Note on Singular Moduli Spaces of Sheaves on K3 Surfaces
• Joyce invariants for K3 surfaces and mock theta functions
• A note on deformations of moduli spaces of sheaves on K3 surfaces
• Correspondences of a K3 surface with itself via moduli of sheaves. I
• Self-correspondences of K3 surfaces via moduli of sheaves and arithmetic hyperbolic reflection groups
• On the Beauville form of the known irreducible symplectic varieties
• A note of moduli of vector bundles on rational surfaces
• On the stabilization of the Betti numbers of the moduli space of sheaves on ${\mathbb{P}}^2$