On the crepancy of the Gieseker-Uhlenbeck morphism. (English) Zbl 1147.14005

Qin, Zhenbo; Zhang, Qi

Asian J. Math. 12, No. 2, 213-224 (2008).

Summary: 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 J. Li [J. Differ. Geom. 37, No. 2, 417–466 (1993; Zbl 0809.14006)]. 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.

MSC:

14D20	Algebraic moduli problems, moduli of vector bundles
14D21	Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
14E05	Rational and birational maps

Keywords:

Gieseker stability; Uhlenbeck compactification; crepant

Citations:

Zbl 0809.14006