Gonality of algebraic curves and graphs
Algebraic Geometry
2013-07-23 v5 Combinatorics
Abstract
We study the interplay between the classical theory of linear series on curves, and the recent theory of linear series on graphs. We prove that every d-gonal (weighted) graph of Hurwitz type is the dual graph of a d-gonal curve. Conversely the dual graph of a d-gonal curve is equivalent to a d-gonal graph. We define d-gonal graphs by what we call harmonic indexed morphisms. Generalizations to higher dimensional linear series, and applications to tropical curves and hyperelliptic graphs are given.
Cite
@article{arxiv.1201.6246,
title = {Gonality of algebraic curves and graphs},
author = {Lucia Caporaso},
journal= {arXiv preprint arXiv:1201.6246},
year = {2013}
}
Comments
Final version to appear in the Springer volume dedicated to Klaus Hulek on the occasion of his 60-th birthday