On metric graphs with prescribed gonality

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:156

Article

Cools, Filip¹  Draisma, Jan^2,3 

[1] Katholieke Univ Leuven, Dept Math, Celestijnenlaan 2006 Box 2400, B-3001 Leuven, Belgium

[2] Univ Bern, Math Inst, Sidlerstr 5, CH-3012 Bern, Switzerland

[3] Tech Univ Eindhoven, Dept Math & Comp Sci, POB 513, NL-5600 MB Eindhoven, Netherlands

关键词: Metric graphs;    Tropical geometry;    Brill-Noether theory;    Gonality;   

DOI  :  10.1016/j.jcta.2017.11.017

来源: Elsevier

【 摘 要 】

We prove that in the moduli space of genus-g metric graphs the locus of graphs with gonality at most d has the classical dimension min {3g - 3, 2g + 2d - 5}. This follows from a careful parameter count to establish the upper bound and a construction of sufficiently many graphs with gonality at most d to establish the lower bound. Here, gonality is the minimal degree of a non-degenerate harmonic map to a tree that satisfies the Riemann-Hurwitz condition everywhere. Along the way, we establish a convenient combinatorial datum capturing such harmonic maps to trees. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free