Blowing-Ups Describing the Polarization Change of Moduli Schemes of Semistable Sheaves of General Rank

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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′) when r is arbitrary and the wall of fixed type separating H and H′ is not necessarily good. Means we here utilize are elementary transforms and the notion of a sheaf with flag.