Stable pairs, linear systems and the Verlinde formula

Details Stable pairs, linear systems and the Verlinde formula Stable pairs, linear systems and the Verlinde formula

1992-10-19

arxiv.org/abs/alg-geom/9210007v1

Mathematics

Algebraic Geometry

40 pages, LaTeX

Scientific paper

We study the moduli problem of pairs consisting of a rank 2 vector bundle and a nonzero section over a fixed smooth curve. The stability condition involves a parameter; as it varies, we show that the moduli space undergoes a sequence of flips in the sense of Mori. As applications, we prove several results about moduli spaces of rank 2 bundles, including the Harder-Narasimhan formula and the SU(2) Verlinde formula. Indeed, we prove a general result on the space of sections of powers of the ideal sheaf of a curve in projective space, which includes the Verlinde formula.

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