Documenta Mathematica· 2026Q1
Wall and chamber structure for a special biserial algebra coming from perverse sheaves on $\mathbb{P}^{n}$
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- 2026year
Short summary
A special biserial algebra derived from perverse sheaves on $\mathbb{P}^n$ is shown to be of finite representation type, with its wall and chamber structure explicitly described and linked to Bridgeland's stability conditions.
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Key points
- The study describes the wall and chamber structure of a special biserial algebra linked to perverse sheaves on $\mathbb{P}^n$.
- The algebra is proven to be of finite representation type.
- An explicit description of the walls of this structure is provided.
- The wall and chamber structure is shown to coincide with Bridgeland's stability condition chambers on the derived category of constructible sheaves on $\mathbb{P}^n$.
AI-generated from the title and abstract; the full text is not read.
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} .
The authors' abstract, as published at the source. Documenta Mathematica, 2026 · DOI ↗
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Field: Geometry and Topology
Geometry and TopologyMathematics