Moduli of Trigonal Curves
| dc.creator | Stankova-Frenkel, Zvezdelina E. | |
| dc.date | 1997-10-12 | |
| dc.date.accessioned | 2026-07-07T01:51:11Z | |
| dc.date.available | 2026-07-07T01:51:11Z | |
| dc.description | We study the moduli of trigonal curves. We establish the exact upper bound of ${36(g+1)}/(5g+1)$ for the slope of trigonal fibrations. Here, the slope of any fibration $X\to B$ of stable curves with smooth general member is the ratio $δ_B/λ_B$ of the restrictions of the boundary class $δ$ and the Hodge class $λ$ on the moduli space $\bar{\mathfrak{M}}_g$ to the base $B$. We associate to a trigonal family $X$ a canonical rank two vector bundle $V$, and show that for Bogomolov-semistable $V$ the slope satisfies the stronger inequality ${δ_B}/{λ_B}\leq 7+{6}/{g}$. We further describe the rational Picard group of the {trigonal} locus $\bar{\mathfrak T}_g$ in the moduli space $\bar{\mathfrak{M}}_g$ of genus $g$ curves. In the even genus case, we interpret the above Bogomolov semistability condition in terms of the so-called Maroni divisor in $\bar{\mathfrak T}_g$. | |
| dc.description | 69 pages, 34 figures, Latex2e | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9710015 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9710015 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/232 | |
| dc.subject | Algebraic Geometry | |
| dc.title | Moduli of Trigonal Curves | |
| dc.type | text |