Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903759 | Journal of Combinatorial Theory, Series A | 2018 | 21 Pages |
Abstract
We prove that in the moduli space of genus-g metric graphs the locus of graphs with gonality at most d has the classical dimensionminâ¡{3gâ3,2g+2dâ5}. 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Filip Cools, Jan Draisma,