Modular compactifications of the space of marked trigonal curves
Algebraic Geometry
2012-06-21 v1
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.
Keywords
Cite
@article{arxiv.1206.4503,
title = {Modular compactifications of the space of marked trigonal curves},
author = {Anand Deopurkar},
journal= {arXiv preprint arXiv:1206.4503},
year = {2012}
}