Abstract
LetS be a smooth projective surface, letK be the canonical class ofS and letH be an ample divisor such thatH • K < 0. We prove that for any rigid sheafF (Ext1 (F, F) = 0) that is Mumford-Takemoto semistable with respect toH there exists an exceptional set (E 1 ,..., E n ) of sheaves onS such thatF can be constructed from {E i } by means of a finite sequence of extensions.
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