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arXiv · 1206.4503

Modular compactifications of the space of marked trigonal curves

Anand Deopurkar
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Abstract

We construct a sequence of modular compactifications of the space of marked trigonal curves by allowing the branch points to coincide to a given extent. Beginning with the standard admissible cover compactification, the sequence first proceeds through contractions of the boundary divisors and then through flips of the so-called Maroni strata, culminating in a Fano model for even genera and a Fano fibration for odd genera. While the sequence of divisorial contractions arises from a more general construction, the sequence of flips uses the particular geometry of triple covers. We explicitly describe the Mori chamber decomposition given by this sequence of flips.

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Anand Deopurkar. 2012-06-20. Modular compactifications of the space of marked trigonal curves. https://arxiv.org/abs/1206.4503

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