Gonality of algebraic curves and graphs

By Lucia Caporaso. 2012

76 citations recorded by the source corpus.

We define d-gonal weighted graphs using “harmonic indexed” morphisms, and prove that a combinatorial locus of \(\overline{M_{g}}\) contains a d-gonal curve if the corresponding graph is d-gonal and of Hurwitz type. Conversely the dual graph of a d-gonal stable curve is equivalent to a d-gonal graph of Hurwitz type. The hyperelliptic case is studied in detail. For r ≥ 1, we show that the dual graph of a (d, r)-gonal stable is the underlying graph of a tropical curve admitting a degree-d divisor of rank at least r.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/87988405799f2daa56bdcd5aed912f0f3a1962f0

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In Algebra and Number Theory

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Lifting harmonic morphisms II: tropical curves and metrized complexes (2014, background): “The closely related, but slightly different, notion of an “indexed harmonic morphism” between weighted graphs was considered in [Caporaso 2014].”