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

Date: 
Tuesday 28th June 2011 - 16:30 to 17:30
Venue: 
INI Seminar Room 1
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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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons