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

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

2007-04-22

arxiv.org/abs/0704.2866v1

J. Math. Kyoto Univ. 43 (2003) no.4, 829-878

Mathematics

Algebraic Geometry

This article has been published, while Introduction is revised

Scientific paper

Let $H$ and $H'$ be two ample line bundles over a nonsingular projective surface $X$, and $M(H)$ (resp. $M(H')$) the coarse moduli scheme of $H$-semistable (resp. $H'$-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 $M(H')$ by a sequence of blowing-ups when walls separating $H$ and $H'$ are not necessarily good. As an application, we also consider the polarization change problem of Donaldson polynomials.

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