Search results for " admissible coverings."

MR 2918162 Reviewed Van der Geer G. and Kouvidakis A. The Hodge bundle on Hurwitz spaces. Pure and Applied Mathematics Quarterly (2011) 7, no. 4, 129…

2012

In this paper the authors consider the Hurwitz space $H_{g, \, d}$ that parametrizes degree $d$ simple coverings of $\mathbb{P}^{1}$ with $b = 2 g - 2 + 2d$ branch points. The compactification $\bar{H}_{g, \, d}$ of this Hurwitz space is the space of admissible covers of genus $g$ and degree $d$, $f: C \rightarrow P$, where $C$ is a nodal curve and $P$ is a stable $b$-pointed curve of genus $0$. Assigning to $f: C \rightarrow P$ the stabilized model of $C$, one defines a natural map $\phi: \bar{H}_{g, \, d} \rightarrow \bar{M}_{g}$ where $\bar{M}_{g}$ denotes the moduli space of stable curves of genus $g$. The Hurwitz space $\bar{H}_{g, \, d}$ carries a natural $\mathbb{Q}$-divisor class, t…