Twisted bundles and admissible covers

Dan Abramovich; Alessio Corti; Angelo Vistoli

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arXiv · math/0106211

Twisted bundles and admissible covers

Dan Abramovich·Alessio Corti·Angelo Vistoli

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Abstract

The cherry on top of this stacky paper is the following: for any g>1 we give a finite group G such that the moduli space of connected admissible G-covers of genus g is a smooth, fine moduli space, which is a Galois cover of the moduli space of stable curves. The proof relies on methods introduced by Looijenga and Pikaart-De Jong, and on the theory of twisted G-covers, a theory announced without proofs in math.AG/9811059, section 3, and developed in the first few sections of this paper. This includes a moduli description of the normalization of the Harris-Mumford space of admissible covers, and a study of moduli of stable curves with abelian and non-abelian level structure.

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Dan Abramovich, Alessio Corti, Angelo Vistoli. 2001-06-25. Twisted bundles and admissible covers. https://arxiv.org/abs/math/0106211

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