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On the structure of semistable rigid sheaves on algebraic surfaces

Boris V. Karpov
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Abstract

Let S be a smooth projective surface, K be the canonical class of S and H be an ample divisor such that H.K<0 . In this paper we prove that for any rigid (Ext^1(F,F)=0) semistable sheaf F in the sense of Mumford--Takemoto stability w.r.t. H there exists an exceptional collection (E_1,...,E_n) of sheaves on S such that F can be constructed from {E_i} by a finite number of extensions.

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Boris V. Karpov. 1995-11-27. On the structure of semistable rigid sheaves on algebraic surfaces. https://arxiv.org/abs/alg-geom/9511017

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