Hurwitz trees and deformations of Artin-Schreier covers
报告人：Huy Dang (University of Virginia)
地点：Zoom ID = 625 5863 1654 , PIN = 809410
Abstract: 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.