Gonality of algebraic curves and graphs

Details Gonality of algebraic curves and graphs Gonality of algebraic curves and graphs

2012-01-30

arxiv.org/abs/1201.6246v2

Mathematics

Algebraic Geometry

Added references and fixed typos. 27 pages

Scientific paper

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 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.

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