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

2007/04/22 by Kimiko Yamada, Yamada, Kimiko
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0704.2870

Abstract

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,c₁,c₂). 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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