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Components of the Stack of Torsion-Free Sheaves of Rank 2 on Ruled Surfaces

Charles H. Walter
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Abstract

Let S be a ruled surface without sections of negative self-intersection. We classify the irreducible components of the moduli stack of torsion-free sheaves of rank 2 sheaves on S. We also classify the irreducible components of the Brill-Noether loci in Hilb^N(P1xP1) given by W_N^0(D)={[X] | h^1(I_X(D)) >= 1 } for D an effective divisor class. Our methods are also applicable to P2 giving new proofs of theorems of Stromme (slightly extended) and Coppo.

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Charles H. Walter. 1993-12-20. Components of the Stack of Torsion-Free Sheaves of Rank 2 on Ruled Surfaces. https://arxiv.org/abs/alg-geom/9312011

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