Geometrical aspects of linear differential equations over compact Riemann surfaces with reductive differential Galois group

Title: Geometrical aspects of linear differential equations over compact Riemann surfaces with reductive differential Galois group
Identifier: d_2009_2013:65aab58e8805:10669
identifier: 10859
Creator: Sanabria Malagon, Camilo,
Contributor: Richard Churchill
Date: 2010
Language: English
Publisher: City University of New York.
Subject: Mathematics | Connections | Differential Algebra | Differential Galois Theory | Ordinary Linear Differential Equations | Riemann Surfaces | Vector Bundles
Abstract: Suppose L(y) = 0 is a linear differential equation with reductive Galois group over the function field of a compact Riemann surface. We prove that any solution to the equation can be written as a product of a solution to a first order equation and a solution to the pullback of an equation of a special form (a "standard equation"). We classify standard equations using ruled surfaces. We relate the symmetries of L(y) = 0 to the outer-automorphisms of the differential Galois group.
Type: dissertation
Source: 2009_2013.csv
degree: Ph.D.
Program: Mathematics

Media: Geometrical aspects of linear differential equations over compact Riemann surfaces with reductive differential Galois group