Semistable sheaves on Del Pezzo surfaces and Kronecker modules

Details Semistable sheaves on Del Pezzo surfaces and Kronecker modules Semistable sheaves on Del Pezzo surfaces and Kronecker modules

1994-09-29

arxiv.org/abs/alg-geom/9409007v1

Mathematics

Algebraic Geometry

21 pages, LATEX, version 2.09

Scientific paper

In this paper we deal with semistable sheaves which can be represented as the cokernel of an injective (or as the kernel of a surjective) morphism $E_1\otimes\CC^m\longrightarrow E_2\otimes\CC^n$ , where $E_1$ and $E_2$ are exceptional bundles. To each such a sheaf we assign the linear map $\CC^m\otimes\hom^*(E_1,E_2)\longrightarrow \CC^n$. We obtain sufficient conditions on the topological invariants of the sheaves for the moduli space of the sheaves to be isomorphic to the quotient of an open subset in $\PP{\cal L}(\CC^m\otimes\hom^*(E_1,E_2),\CC^n)$ under the action of SL$(\CC^m)\times$SL$(\CC^n)$.

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