Wall and chamber structure for a special biserial algebra coming from perverse sheaves on $\mathbb{P}^{n}$

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} .

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Publication Details

Journal
Documenta Mathematica
Published
2026-10-15
DOI
https://doi.org/10.4171/dm/1096
Primary Topic
Algebraic structures and combinatorial models
Type
article
Field-Weighted Citation Impact
0.00

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article

Wall and chamber structure for a special biserial algebra coming from perverse sheaves on $\mathbb{P}^{n}$

Alessio Cipriani, Martina Lanini
2 links
Documenta Mathematica
Algebraic structures and combinatorial models
article

Wall and chamber structure for a special biserial algebra coming from perverse sheaves on $\mathbb{P}^{n}$

Alessio Cipriani, Martina Lanini
article en

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} .

Documenta Mathematica
University of Rome Tor Vergata (IT), University of Verona (IT)
Istituto Nazionale di Alta Matematica "Francesco Severi", Fondazione Cassa di Risparmio di Verona Vicenza Belluno e Ancona, Università degli Studi di Roma Tor Vergata
Openalex Percentile: Top 97%
Algebraic structures and combinatorial models
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