### Koszul cohomology and higher rank vector bundles on curves

Farkas, G *(Humboldt)*

Thursday 24 March 2011, 15:30-16:30

Seminar Room 2, Newton Institute Gatehouse

#### Abstract

Some years ago V. Mercat proposed an interesting conjecture relating the Clifford index of a curve C (which measures the complexity of C in its moduli space) to stable vector bundles of higher rank on C. Even though some counterexamples have been found, Mercat's Conjecture is still expected to hold for a general curve, and the failure locus of the conjecture gives rise to new extremal divisors in the moduli space of curves.
I will explain the general problem and discuss a Koszul-theoretic approach to Mercat's prediction.