Moduli of Representations of Skewed-Gentle Algebras

TL;DR

This paper demonstrates that the irreducible components of moduli spaces of semistable representations for skewed-gentle and clannish algebras are isomorphic to products of projective spaces, generalizing previous results for special biserial algebras.

Contribution

It establishes the normality of irreducible components of representation varieties for skewed-gentle algebras and generalizes known results to a broader class of algebras.

Findings

Irreducible components are isomorphic to products of projective spaces.

Irreducible components of clannish algebra representations can be viewed as those of skewed-gentle algebras.

Irreducible components of skewed-gentle algebras are always normal.

Abstract

We prove irreducible components of moduli spaces of semistable representations of skewed-gentle algebras, and more generally, clannish algebras, are isomorphic to products of projective spaces. This is achieved by showing irreducible components of varieties of representations of clannish algebras can be viewed as irreducible components of skewed-gentle algebras, which we show are always normal. The main theorem generalizes an analogous result for moduli of representations of special biserial algebras proven by Carroll-Chindris-Kinser-Weyman.