Hurwitz Trees and Deformations of Artin-Schreier Covers
Time: 2020-05-14
Published By: He Liu
Speaker(s): Huy Dang (University of Virginia)
Time: 13:00-14:00 May 20, 2020
Venue: Online
In this talk, we introduce the notion of Hurwitz tree for an Artin-Schreier deformation (deformation of Z/p-covers in characteristic p>0 ). It is a combinatorial-differential object that is endowed with essential degeneration data, measured by Kato's refined Swan conductors, of the deformation. We then show how the existence of a deformation between two covers with different branching data (e.g., different number of branch points) equates to the presence of a Hurwitz tree with behaviors determined by the branching data. One application of this result is to prove that the moduli space of Artin-Schreier covers of fixed genus g is connected when g is sufficiently large. If time permits, we will discuss a generalization of the Hurwitz tree technique to all cyclic covers and beyond.
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