Irreducibility of Moduli Spaces of Vector Bundles on Birationally Ruled Surfaces

Details Irreducibility of Moduli Spaces of Vector Bundles on Birationally Ruled Surfaces Irreducibility of Moduli Spaces of Vector Bundles on Birationally Ruled Surfaces

1993-11-16

arxiv.org/abs/alg-geom/9311005v1

Mathematics

Algebraic Geometry

7 pages, LATeX 2.09

Scientific paper

Let $S$ be a birationally ruled surface. We show that the moduli schemes $M_S(r,c_1,c_2)$ of semistable sheaves on $S$ of rank $r$ and Chern classes $c_1$ and $c_2$ are irreducible for all $(r,c_1,c_2)$ provided the polarization of $S$ used satisfies a simple numerical condition. This is accomplished by proving that the stacks of prioritary sheaves on $S$ of fixed rank and Chern classes are smooth and irreducible.

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