The Koszul geometry of moduli spaces
Gavril Farkas (Humboldt University of Berlin)

Given a moduli space, what is the "best" effective divisor one can construct on it? We present a very general method of constructing divisors on moduli spaces using the syzygies of the parameterized objects. Applications of this method include:
(1) a proof that the moduli space of curves of genus 22 is of general type, and
(2) a proof that the moduli space S_g of curves of genus g together with an even theta-characteristic is of general type for g > 8.

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