2012/06/20 by Anand Deopurkar, Deopurkar, Anand
Mathematics · #14H10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #math.AG #msc:14H10
paper · pdf · doi:10.48550/arxiv.1206.4503
arxiv created 2012/06/20 · openalex publication_date 2012/06/20 · arxiv updated 2012/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.