On the Crepancy of the Gieseker-Uhlenbeck Morphism

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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Published 1 January 2008