Bulletin of the Belgian Mathematical Society - Simon Stevin

The Fermat cubic and special Hurwitz loci in $\overline{\mathcal{M}}_g$

Gavril Farkas

Abstract

We compute the class of the compactified Hurwitz divisor $\overline{\mathfrak{TR}}_d$ in $\overline{\mathcal{M}}_{2d-3}$ consisting of curves of genus $g=2d-3$ having a pencil $\mathfrak g^1_d$ with two unspecified triple ramification points. This is the first explicit example of a geometric divisor on $\overline{\mathcal{M}}_g$ which is not pulled-back form the moduli space of pseudo-stable curves. We show that the intersection of $\overline{\mathfrak{TR}}_d$ with the boundary divisor $\Delta_1$ in $\overline{\mathcal{M}}_g$ picks-up the locus of Fermat cubic tails.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 16, Number 5 (2009), 831-851.

Dates
First available in Project Euclid: 9 December 2009

https://projecteuclid.org/euclid.bbms/1260369402

Digital Object Identifier
doi:10.36045/bbms/1260369402

Mathematical Reviews number (MathSciNet)
MR2574363

Zentralblatt MATH identifier
1184.14041

Subjects
Primary: 14H10: Families, moduli (algebraic)

Citation

Farkas, Gavril. The Fermat cubic and special Hurwitz loci in $\overline{\mathcal{M}}_g$. Bull. Belg. Math. Soc. Simon Stevin 16 (2009), no. 5, 831--851. doi:10.36045/bbms/1260369402. https://projecteuclid.org/euclid.bbms/1260369402