Asian Journal of Mathematics

Volume 12 (2008)

Number 2

On the Crepancy of the Gieseker-Uhlenbeck Morphism

Pages: 213 – 224

DOI: http://dx.doi.org/10.4310/AJM.2008.v12.n2.a5

Authors

Zhenbo Qin

Qi Zhang

Abstract

The Gieseker-Uhlenbeck morphism from the moduli space of Gieseker semistable rank-2 sheaves over an algebraic surface to the Uhlenbeck compactification was constructed by Jun Li. We prove that if the anti-canonical divisor of the surface is effective and the first Chern class of the semistable sheaves is odd, then the Gieseker-Uhlenbeck morphism is crepant

Keywords

Gieseker stability; Uhlenbeck compactification; crepant

2010 Mathematics Subject Classification

Primary 14D20. Secondary 14D21, 14E05.

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