On the structure of semistable rigid sheaves on algebraic surfaces
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 (Ext1(F,F)=0) semistable sheaf F in the sense of Mumford--Takemoto stability w.r.t. H there exists an exceptional collection (E1,...,En) of sheaves on S such that F can be constructed from Ei by a finite number of extensions.
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