Asian Journal of Mathematics

The class of a Hurwitz divisor on the moduli of curves of even genus

Gerard van der Geer and Alexis Kouvidakis

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Abstract

We study the geometry of the natural map from the Hurwitz space $\overline{H}_{2k,k+1}$ to the moduli space $\overline{\mathcal{M}}_{2k}$. We calculate the cycle class of the Hurwitz divisor $D_2$ on $\overline{\mathcal{M}}_g$ for $g = 2k$ given by the degree $k + 1$ covers of $\mathbb{P}^1$ with simple ramification points, two of which lie in the same fibre. This has applications to bounds on the slope of the moving cone of $\overline{\mathcal{M}}_g$, the calculation of other divisor classes and motivated an algebraic proof for the formula of the Hodge bundle of the Hurwitz space.

Article information

Source
Asian J. Math., Volume 16, Number 4 (2012), 787-806.

Dates
First available in Project Euclid: 12 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1355321987

Mathematical Reviews number (MathSciNet)
MR3004286

Zentralblatt MATH identifier
1263.14035

Subjects
Primary: 14H10: Families, moduli (algebraic) 14H51: Special divisors (gonality, Brill-Noether theory)

Keywords
Hurwitz space Hurwitz divisor moduli of curves

Citation

van der Geer, Gerard; Kouvidakis, Alexis. The class of a Hurwitz divisor on the moduli of curves of even genus. Asian J. Math. 16 (2012), no. 4, 787--806. https://projecteuclid.org/euclid.ajm/1355321987


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