Jerzy M. Weyman
Jerzy M. Weyman, Gordana G. Todorov, Donald King, Calin Chindris
Date of Award
Doctor of Philosophy
Department or Academic Unit
College of Science, Department of Mathematics
canonical decomposition, generic representation, GIT quotients, schur module, semi-invariant
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.
Andrew Thomas Carroll
Carroll, Andrew Thomas, "Semi-invariants for gentle string algebras" (2012). Mathematics Dissertations. Paper 18. http://hdl.handle.net/2047/d20002384
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