Irreducibility of Moduli Spaces of Vector Bundles on Birationally Ruled Surfaces

1993/11/16 by Charles Walter, Walter, Charles · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9311005

7 pages, LATeX 2.09

arxiv created 1993/11/16 · arxiv updated 2009/11/30

Abstract

Let S be a birationally ruled surface. We show that the moduli schemes M_S(r,c₁,c₂) of semistable sheaves on S of rank r and Chern classes c₁ and c₂ are irreducible for all (r,c₁,c₂) 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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