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Koszul cohomology and higher rank vector bundles on curves

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If you have a question about this talk, please contact Burt Totaro .

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.

This talk is part of the Algebraic Geometry Seminar series.

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