Wall And Chamber Structure For A Special Biserial Algebra Coming From Perverse Sheaves on ℙⁿ

2023/08/02 by Alessio Cipriani, Cipriani, Alessio, Martina Lanini +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Rings, Modules, and Algebras #math.AG #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.2308.00991

openalex publication_date 2023/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

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 ℙⁿ. 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 ℙⁿ.

Related

• Sheaves on the alcoves I: Projectivity and wall crossing functors
• Bridgeland walls destabilizing one-dimensional space sheaves
• Sheaves on the alcoves and modular representations I
• Mini-walls for Bridgeland stability conditions on the derived category of sheaves over surfaces
• Stacks similar to the stack of perverse sheaves