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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/149857Let 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.16 pages, LATeX 2.09Algebraic GeometryComponents of the Stack of Torsion-Free Sheaves of Rank 2 on Ruled Surfacestext