Wall And Chamber Structure For A Special Biserial Algebra Coming From Perverse Sheaves on $\mathbb{P}^n$

TL;DR

This paper analyzes the wall and chamber structure of a special biserial algebra linked to perverse sheaves on complex projective space, revealing its finite representation type and explicit wall description.

Contribution

It provides a detailed description of the wall and chamber structure for a specific algebra related to perverse sheaves, connecting it to stability conditions.

Findings

Algebra is of finite representation type

Explicit description of walls in the structure

Connection to stability conditions on derived categories

Abstract

We describe the wall and chamber structure of a special biserial algebra whose module category is equivalent to the category of (middle) perverse sheaves on the complex projective space $\mathbb{P}^n$. In particular, by the well known classification of indecomposable modules for special biserial algebras, we deduce that the algebra of interest is of finite representation type and we provide an explicit description of the walls of the structure. By a result of Bridgeland this wall and chamber structure coincides with the chamber structure in an open subset of the space of stability conditions on the bounded derived category of constructible sheaves on $\mathbb{P}^n$.