Maps between moduli spaces of curves and Gieseker-Petri divisors

Maps between moduli spaces of curves and Gieseker-Petri divisors

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Gavril Farkas, Humboldt Universität zu Berlin
Fine Hall 322

We study contractions of the moduli space of stable curves beyond the minimal model of M_g by resolving and giving a complete enumerative description of the rational map between moduli spaces of curves Mg --> Mh which associates to a curve C of genus g, the Brill-Noether locus of special divisors in the case this locus is a curve. As an application we construct myriads of moving effective divisors on M_g of small slope. For low g, our calculation can be used to study the intersection theory of the moduli space of Prym varieties of dimension 5.