Divisorial and geometric gonality of higher-rank tropical curves

Autor:	de Bruyn, Josse van Dobben, Holmes, David, van der Vorm, David
Rok vydání:	2021
Předmět:	Mathematics - Combinatorics Mathematics - Algebraic Geometry
Druh dokumentu:	Working Paper
Popis:	We consider a variant of metrised graphs where the edge lengths take values in a commutative monoid, as a higher-rank generalisation of the notion of a tropical curve. Divisorial gonality, which Baker and Norine defined on combinatorial graphs in terms of a chip firing game, is extended to these monoid-metrised graphs. We define geometric gonality of a monoid-metrised graph as the minimal degree of a horizontally conformal, non-degenerate morphism onto an monoid-metrised tree, and prove that geometric gonality is an upper bound for divisorial gonality in the monoid-metrised case. We also show the existence of a subdivision of the underlying graph whose gonality is no larger than the monoid-metrised gonality. We relate this to the minimal degree of a map between logarithmic curves. Comment: 17 pages; comments very welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2112.04205 Zobrazit plný text záznamu View this record from Arxiv