Jeffrey Yelton, Wesleyan University
Event Date
2026-04-01
Event Time
03:25 pm ~ 04:45 pm
Event Location
Wachman 413
Let K be a field with a nonarchimedean valuation, and let C be a curve over K defined by an equation of the form y^p = f(x), where p is any prime (which is allowed to be the residue characteristic of K). The shape of a semistable model of such a curve can be determined from the cluster data of the roots of the polynomial f. I will explain a way to encode such cluster data as a metric graph and, using this framework, provide a criterion for C to have a special geometric property called split degenerate reduction. Meanwhile, this property is equivalent to C being uniformizable as a certain subset of the projective line modulo the action of a group of fractional linear transformations. I will use this uniformization to demonstrate another perspective on the cluster data of a superelliptic curve with split degenerate reduction.