This article is cited in 13 papers

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

N. V. Timofeeva<sup>ab

a</sup> P. G. Demidov Yaroslavl State University
^b Yaroslavl State Pedagogical University named after K. D. Ushinsky

Abstract: We construct a new compactification of the moduli scheme of Gieseker-stable vector bundles having fixed Hilbert polynomial on a smooth projective polarized surface $(S,H)$ defined over the field $k=\mathbb C$. 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. We consider the case when the Gieseker-Maruyama space is the coarse moduli space.
Bibliography: 16 titles.

Keywords: moduli space, semistable coherent sheaves, pseudofamily, algebraic surface.

UDC: 512.722+512.723

MSC: 14J60

Received: 08.04.2008 and 24.11.2008

DOI: 10.4213/sm5234

 English version: Sbornik: Mathematics, 2009, 200:3, 405–427

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