Moduli of Trigonal Curves
Zvezdelina E. Stankova-Frenkel

TL;DR
This paper investigates the moduli space of trigonal curves, establishing bounds on the slope of trigonal fibrations, analyzing associated vector bundles, and describing the Picard group of the trigonal locus.
Contribution
It provides the exact upper bound for the slope of trigonal fibrations and relates Bogomolov-semistability to geometric divisors in the moduli space.
Findings
Established the upper bound ${36(g+1)}/(5g+1)$ for the slope.
Linked Bogomolov-semistability to the Maroni divisor in even genus cases.
Described the rational Picard group of the trigonal locus in the moduli space.
Abstract
We study the moduli of trigonal curves. We establish the exact upper bound of for the slope of trigonal fibrations. Here, the slope of any fibration of stable curves with smooth general member is the ratio of the restrictions of the boundary class and the Hodge class on the moduli space to the base . We associate to a trigonal family a canonical rank two vector bundle , and show that for Bogomolov-semistable the slope satisfies the stronger inequality . We further describe the rational Picard group of the {trigonal} locus in the moduli space of genus curves. In the even genus case, we interpret the above Bogomolov semistability condition in terms of the so-called Maroni divisor in $\bar{\mathfrak…
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Algebraic Geometry and Number Theory · Polynomial and algebraic computation
