Abstract
A new compactification for the scheme of moduli for Gieseker-stable vector bundles with prescribed Hilbert polynomial on the smooth projective polarized surface is constructed. We work over the field of characteristic zero. Families of locally free sheaves on the surface are completed with locally free sheaves on schemes which are modifications of . The Gieseker-Maruyama moduli space has a birational morphism onto the new moduli space. We propose the functor for families of pairs 'polarized scheme-vector bundle' with moduli space of such type.Bibliography: 16 titles.
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