Hurwitz Trees and Tropical Geometry
Abstract
The lifting problem in algebraic geometry asks when a finite group G acting on a curve
defined over characteristic p > 0 lifts to characteristic 0. One object used in the study of
this problem is the Hurwitz tree, which encodes the ramification data of a group action
on a disk. In this thesis we explore the connection between Hurwitz trees and tropical
geometry. That is, we can view the Hurwitz tree as a tropical curve. After exploring
this connection we provide two examples to illustrate the connection, using objects in
tropical geometry to demonstrate when a group action fails to lift.
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Cite this version of the work
Garnet Jonathan Akeyr
(2016).
Hurwitz Trees and Tropical Geometry. UWSpace.
http://hdl.handle.net/10012/10186
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