On the gonality of metric graphs

Draisma, Jan; Vargas, Alejandro (2021). On the gonality of metric graphs. Notices of the American Mathematical Society, 68(5), pp. 687-695. American Mathematical Society 10.1090/noti2277

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The last decades have seen an extremely fruitful interplay between Riemann surfaces and graphs with a metric. A deformation process called tropicalisation transforms the former into the latter. Under this process, additional structure on the Riemann surfaces yields additional structure on the metric graphs. For instance, meromorphic functions on Riemann surfaces yield piecewise linear functions on metric graphs. In this manner, theorems in algebraic geometry have deep combinatorial consequences; and conversely, combinatorial arguments can be used to prove theorems in algebraic geometry.

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