Dual Graphs and Poincare Series of Valuations

Title: Dual Graphs and Poincare Series of Valuations
Identifier: d_2009_2013:99738d8b2362:11367
identifier: 11672
Creator: Li, Charles,
Contributor: Hans Schoutens
Date: 2012
Language: English
Publisher: City University of New York.
Subject: Mathematics | dual graphs | generating sequences | poincare series | spivakovsky | valuations | valuation theory
Abstract: Valuations on function fields of dimension two have been studied from the perspectives of dual graphs, generating sequences, Poincare series, and the valuative tree, among others. The goal of this dissertation is to greater unify these various approaches. Spivakovsky's dual graphs are used to calculate the Poincare series of non-divisorial valuations. With Galindo's results in the divisorial case already known, the equivalence of Poincare series with dual graphs is shown. A new elementary constructive proof of minimal generating sequences for non-divisorial valuations is given along the way, using only modest prerequisites from number theory. It is fair to say that the proof of minimal generating sequences is the crux of this dissertation, while the results on Poincare series are all corollaries.
Type: dissertation
Source: 2009_2013.csv
degree: Ph.D.
Program: Mathematics