Asian Journal of Mathematics
Volume 12 (2008)
On the Crepancy of the Gieseker-Uhlenbeck Morphism
Pages: 213 – 224
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
Gieseker stability; Uhlenbeck compactiﬁcation; crepant
2010 Mathematics Subject Classification
Primary 14D20. Secondary 14D21, 14E05.