We show that a moduli space of slope-stable coherent sheaves over a K3 surface is a compact hyperkahler manifold if and only if its second Betti number is the sum of its Hodge numbers h^{2,0}, h^{1,1} and h^{0,2}. .
Kahlerness of moduli spaces of stable sheaves over non-projective K3 surfaces
Arvid Perego
2019-01-01
Abstract
We show that a moduli space of slope-stable coherent sheaves over a K3 surface is a compact hyperkahler manifold if and only if its second Betti number is the sum of its Hodge numbers h^{2,0}, h^{1,1} and h^{0,2}. .
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