Mathematics – Algebraic Geometry
Scientific paper
2007-11-08
Bulletin of the Belgian Mathematical Society "Simon Stevin" 5 (2009), 831-851
Mathematics
Algebraic Geometry
19 pages. To appear in the Proceedings of the Conference "Linear systems and subschemes" (Ghent 2007), published by the Bullet
Scientific paper
We compute the class of the locus in M_g of curves having a pencil with two unspecified triple ramification points. This is the first example of a geometric divisor on M_g which is not the pull-back of a divisor on the moduli space of pseudo-stable curves. This space, in which elliptic tails are replaced by cusps, appears as a result of the first divisorial contraction in the minimal model program for M_g. In particular, we show that our divisor picks-up the locus of Fermat cubic tails when restricted to the boundary divisor of elliptic tails. We also give various enumerative applications concerning coverings of the generic curve having special ramification behaviour.
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