On the structure of semistable rigid sheaves on algebraic surfaces

Details On the structure of semistable rigid sheaves on algebraic surfaces On the structure of semistable rigid sheaves on algebraic surfaces

1995-11-27

arxiv.org/abs/alg-geom/9511017v1

Mathematics

Algebraic Geometry

LaTeX v 2.09. 8 pages

Scientific paper

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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