Geodesic
On a new compactification of moduli of vector bundles on a surface.
Sbornik. Mathematics, Tome 202 (2011) no. 3, pp. 413-465

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A new compactification for the scheme of moduli for Gieseker-stable vector bundles with prescribed Hilbert polynomial on the smooth projective polarized surface $(S,L)$ is constructed. We work over the field $k=\bar k$ of characteristic zero. Families of locally free sheaves on the surface $S$ are completed with locally free sheaves on schemes which are modifications of $S$. 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.
Keywords: semistable coherent sheaves, moduli functor
Mots-clés : moduli space, algebraic surface. 
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N. V. Timofeeva. On a new compactification of moduli of vector bundles on a surface.. Sbornik. Mathematics, Tome 202 (2011) no. 3, pp. 413-465. http://geodesic.mathdoc.fr/item/SM_2011_202_3_a4/