# Moduli spaces of representations of special biserial algebras

## TL;DR

This paper proves that moduli spaces of semistable representations of special biserial algebras decompose into products of projective spaces, revealing their geometric structure and normality.

## Contribution

It establishes the isomorphism between irreducible components of these moduli spaces and products of projective spaces, using properties of varieties of circular complexes.

## Key findings

- Irreducible components are isomorphic to products of projective spaces.
- Varieties of representations are isomorphic to products of circular complexes.
- Moduli spaces are normal and decomposable into well-understood geometric objects.

## Abstract

We show that the irreducible components of any moduli space of semistable representations of a special biserial algebra are always isomorphic to products of projective spaces of various dimensions. This is done by showing that irreducible components of varieties of representations of special biserial algebras are isomorphic to irreducible components of products of varieties of circular complexes, and therefore normal, allowing us to apply recent results of the second and third authors on moduli spaces.