Irreducibility of Moduli Spaces of Vector Bundles on Birationally Ruled Surfaces

Abstract

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.

7 pages, LATeX 2.09

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• Interpolation and moduli spaces of vector bundles on very general blowups of the projective plane
• Birational classification of moduli spaces of vector bundles over ${\mathbb{P}}^2$