This article is cited in 11 papers

On a new compactification of moduli of vector bundles on a surface. III: Functorial approach

N. V. Timofeeva

P. G. Demidov Yaroslavl State University

Abstract: 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: moduli space, semistable coherent sheaves, moduli functor, algebraic surface.

UDC: 512.722+512.723

MSC: Primary 14J60; Secondary 14D20, 14M27

Received: 13.11.2009 and 29.06.2010

DOI: 10.4213/sm7652

 English version: Sbornik: Mathematics, 2011, 202:3, 413–465

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