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December 2012 The class of a Hurwitz divisor on the moduli of curves of even genus
Gerard van der Geer, Alexis Kouvidakis
Asian J. Math. 16(4): 787-806 (December 2012).

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.

Citation

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Gerard van der Geer. Alexis Kouvidakis. "The class of a Hurwitz divisor on the moduli of curves of even genus." Asian J. Math. 16 (4) 787 - 806, December 2012.

Information

Published: December 2012
First available in Project Euclid: 12 December 2012

zbMATH: 1263.14035
MathSciNet: MR3004286

Subjects:
Primary: 14H10, 14H51

Rights: Copyright © 2012 International Press of Boston

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Vol.16 • No. 4 • December 2012
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