| 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. |
