On metric graphs with prescribed gonality

Cools, Filip; Draisma, Jan (2018). On metric graphs with prescribed gonality. Journal of combinatorial theory. Series A, 156, pp. 1-21. Elsevier 10.1016/j.jcta.2017.11.017

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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 - 5g}: This follows from a careful parameter count to establish the upper bound and a construction of suffciently 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

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Draisma, Jan

Subjects:

500 Science > 510 Mathematics

ISSN:

0097-3165

Publisher:

Elsevier

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

08 May 2019 10:38

Last Modified:

25 Oct 2019 00:14

Publisher DOI:

10.1016/j.jcta.2017.11.017

BORIS DOI:

10.7892/boris.125491

URI:

https://boris.unibe.ch/id/eprint/125491

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