## 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.

Original language | English |
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Pages (from-to) | 96-154 |

Number of pages | 59 |

Journal | Advances in Mathematics |

Volume | 248 |

DOIs | |

Publication status | Published - 25 Nov 2013 |

Externally published | Yes |