DESINGULARIZATION AND SINGULARITIES OF SOME MODULI SCHEME OF SHEAVES ON A SURFACE

Let X be a nonsingular projective surface over C, and H- and H+ be ample line bundles on X in adjacent chamber of type (c(1),c(2)).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 (c(1),c(2)) 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.