Advisor(s)

Jerzy M. Weyman

Contributor(s)

Jerzy M. Weyman, Gordana G. Todorov, Donald King, Calin Chindris

Date of Award

1-2012

Date Accepted

1-2012

Degree Grantor

Northeastern University

Degree Level

Ph.D.

Degree Name

Doctor of Philosophy

Department or Academic Unit

College of Science, Department of Mathematics

Keywords

canonical decomposition, generic representation, GIT quotients, schur module, semi-invariant

Disciplines

Mathematics

Abstract

This thesis is devoted to the study of the geometry of representation spaces of string algebras. For each irreducible component C of a representation space of a gentle string algebra, we give an algorithm to determine the ring of semi-invariant functions on C. We show that these rings are semigroup rings (even coordinate rings of toric varieties) whose generators and relations can be described as walks on a particular graph. In addition, we determine the canonical decompositions of the modules in C. This decomposition allows a general discussion of the generating semi-invariants via Schofield's construction. This decomposition can be used to describe certain important GIT quotients for particular choices of C.

Document Type

Dissertation

Rights Holder

Andrew Thomas Carroll


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