Rational maps between moduli spaces of curves and Gieseker-Petri divisors

Details Rational maps between moduli spaces of curves and Gieseker-Petri divisors Rational maps between moduli spaces of curves and Gieseker-Petri divisors

2007-08-30

arxiv.org/abs/0708.4188v3

Journal of Algebraic Geometry 19 (2010), 243-284

Mathematics

Algebraic Geometry

34 pages. Minor corrections. To appear in the Journal of Algebraic Geometry

Scientific paper

We perform an intersection theoretic study of the rational map between two different moduli spaces of stable curves which associates to a curve its corresponding Brill-Noether locus (in the case this locus has virtual dimension 1). We then use these results to describe the cone of moving divisors on M_g. Several other applications to moduli spaces of Prym varieties are presented. In a different direction, we prove that the locus in M_g of curves failing to satisfy the Gieseker-Petri theorem is supported in codimension 1 for every possible type of linear series.

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