Desingularization and Singularities of Some Moduli Scheme of Sheaves on a Surface

Abstract

Let X be a nonsingular projective surface over C, and H_{-} and H_{+} be ample line bundles on X in adjacent chamber of type (c1; c2). Let 0 < a_{-} < a_{+} < 1 be adjacent minichambers, which are defined from H_{-} and H_{+}, such that the moduli scheme M(H_{-}) of rank-two a_{-}-stable sheaves with Chern classes (c1; c2) is non-singular. We shall construct a desingularization of M(a_{+}) by using M(a_{-}). As an application, we study whether singularities of M(a_{+}) are terminal or not in some cases where X is ruled or elliptic.