On the crepancy of the Gieseker-Uhlenbeck morphism

摘要

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 [Li1] (see also [Uhl, Mor]). 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.