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 Koszultheoretic approach
to Mercat’s prediction.
This talk is part of the Algebraic Geometry Seminar series.
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