Geodesic
On the structure of rigid semistable sheaves on algebraic surfaces
Matematičeskie zametki, Tome 64 (1998) no. 5, pp. 692-700.

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Let $S$ be a smooth projective surface, let $K$ be the canonical class of $S$ and let $H$ be an ample divisor such that $H\cdot K0$. We prove that for any rigid sheaf $F$ ($\operatorname{Ext}^1(F,F)=0$) that is Mumford–Takemoto semistable with respect to $H$ there exists an exceptional set $(E_1,\dots,E_n)$ of sheaves on $S$ such that $F$ can be constructed from $\{E_i\}$ by means of a finite sequence of extensions. 
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     author = {B. V. Karpov},
     title = {On the structure of rigid semistable sheaves on algebraic surfaces},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {5},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_5_a5/}
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B. V. Karpov. On the structure of rigid semistable sheaves on algebraic surfaces. Matematičeskie zametki, Tome 64 (1998) no. 5, pp. 692-700. http://geodesic.mathdoc.fr/item/MZM_1998_64_5_a5/

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