Desingularization of some moduli scheme of stable sheaves on a surface

Abstract

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.