On a new compactification of the moduli of vector bundles on a surface

A new compactification of the moduli scheme of Gieseker-stable vector bundles with prescribed Hilbert polynomial on a smooth projective polarized surface $(S,H)$ defined over a field $k=\bar k$ of characteristic zero is constructed. The families of locally free sheaves on the surface $S$ are completed by locally free sheaves on surfaces that are certain modifications of $S$. The new moduli space has a birational morphism onto the Gieseker-Maruyama moduli space. The case when the Gieseker-Maruyama space is a fine moduli space is considered.
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