A sequence of blowing-ups connecting moduli of sheaves and the Donaldson polynomial under change of polarization

Abstract

Let $H$ and $H^{\prime }$ be two ample line bundles over a nonsingular projective surface $X$, and $M(H)$ (resp. $M(H^{\prime })$) the coarse moduli scheme of $H$-semistable (resp. $H^{\prime }$-semistable) sheaves of fixed type $(r=2,c_1,c_2)$. In a moduli-theoretic way that comes from elementary transforms, we connect $M(H)$ and $M(H^{\prime })$ by a sequence of blowing-ups when walls separating $H$ and $H^{\prime }$ are not necessarily good. As an application, we also consider the polarization change problem of Donaldson polynomials.

This article has been published, while Introduction is revised