Compact Moduli Spaces of Stable Sheaves over Non-Algebraic Surfaces

We show that under certain conditions on the topological invariants, the moduli spaces of stable bundles over polarized non-algebraic surfaces may be compactified by allowing at the border isomorphy classes of stable non-necessarily locally-free sheaves. As a consequence, when the base surface is a primary Kodaira surface, we obtain examples of moduli spaces of stable sheaves which are compact holomorphically symplectic manifolds.

2000 Mathematics Subject Classification: 32C13

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