Desingularization of some moduli scheme of stable sheaves on a surface

Details Desingularization of some moduli scheme of stable sheaves on a surface Desingularization of some moduli scheme of stable sheaves on a surface

2008-09-18

arxiv.org/abs/0809.3068v1

Mathematics

Algebraic Geometry

Scientific paper

Let $X$ be a nonsingular projective surface over an algebraically closed field with characteristic zero, and $H_-$ and $H_+$ ample line bundles on $X$ separated by only one wall of type $(c_1,c_2)$. Suppose the moduli scheme $M(H_-)$ of rank-two $H_-$-stable sheaves with Chern classes $(c_1,c_2)$ is non-singular. We shall construct a desingularization of $M(H_+)$ by using $M(H_-)$. As an application, we consider whether singularities of $M(H_+)$ are terminal or not when $X$ is ruled or elliptic.

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