Irreducibility of the moduli space of vector bundles on surfaces and Brill-Noether theory on singular curves

Details Irreducibility of the moduli space of vector bundles on surfaces and Brill-Noether theory on singular curves Irreducibility of the moduli space of vector bundles on surfaces and Brill-Noether theory on singular curves

1997-10-27

arxiv.org/abs/alg-geom/9710029v2

Mathematics

Algebraic Geometry

Revised PhD thesis (Princeton, 1997), 64 pages, 1 figure, LaTeX2e, Xy-pic

Scientific paper

We prove the irreducibility of the moduli space of rank 2 semistable torsion free sheaves (with a generic polarization and any value of c_2) on a K3 or a del Pezzo surface. In the case of a K3 surface, we need to prove a result on the connectivity of the Brill-Noether locus for singular curves on the surface. In the case of a del Pezzo surface, we reduce the problem to the case of P^2 by first relating the moduli spaces of the plane and the blown-up plane, and then studying how the moduli space changes when we change the polarization.

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