Hurwitz Trees and Tropical Geometry

geometry;arithmetic;curves;combinatorics

Akeyr, Garnet Jonathan

University of Waterloo

关键词: geometry;    arithmetic;    curves;    combinatorics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/10186/3/Akeyr_Garnet.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

The lifting problem in algebraic geometry asks when a finite group G acting on a curvedefined over characteristic p > 0 lifts to characteristic 0. One object used in the study ofthis problem is the Hurwitz tree, which encodes the ramification data of a group actionon a disk. In this thesis we explore the connection between Hurwitz trees and tropicalgeometry. That is, we can view the Hurwitz tree as a tropical curve. After exploringthis connection we provide two examples to illustrate the connection, using objects intropical geometry to demonstrate when a group action fails to lift.