Blowing-ups describing the polarization change of moduli schemes of semistable sheaves of general rank

Details Blowing-ups describing the polarization change of moduli schemes of semistable sheaves of general rank Blowing-ups describing the polarization change of moduli schemes of semistable sheaves of general rank

2007-04-22

arxiv.org/abs/0704.2870v1

Mathematics

Algebraic Geometry

Scientific paper

Let $H$ and $H'$ be two ample line bundles over a smooth projective surface $X$, and $M(H)$ (resp. $M(H')$) the coarse moduli scheme of $H$-semistable (resp. $H'$-semistable) sheaves of fixed type $(r,c_1,c_2)$. We construct a sequence of blowing-ups which describes how $M(H)$ differs from $M(H')$ not only when $r=2$ but also when $r$ is arbitrary. Means we here utilize are elementary transforms and the notion of a sheaf with flag.

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