Components of the Stack of Torsion-Free Sheaves of Rank 2 on Ruled Surfaces
Charles H. Walter
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 HilbN(P1xP1) given by WN0(D)=[X] | h1(IX(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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