### Rank two Brill-Noether theory and the birational geometry of the moduli space of curves

Farkas, G *(Humboldt)*

Tuesday 28 June 2011, 16:30-17:30

Seminar Room 1, Newton Institute

#### Abstract

I shall discuss applications of Koszul cohomology and rank two Brill-Noether theory to the intersection theory of the moduli space of curves. For instance, one can construct extremal divisors in M_g whose points are characterized in terms of existence of certain rank two vector bundles. I shall then explain how these subvarieties of M_g can be thought of as failure loci of an interesting prediction of Mercat in higher rank Brill-Noether theory.

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