English

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

Representation Theory 2023-08-03 v1 Algebraic Geometry Combinatorics

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\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 Pn\mathbb{P}^n.

Keywords

Cite

@article{arxiv.2308.00991,
  title  = {Wall And Chamber Structure For A Special Biserial Algebra Coming From Perverse Sheaves on $\mathbb{P}^n$},
  author = {Alessio Cipriani and Martina Lanini},
  journal= {arXiv preprint arXiv:2308.00991},
  year   = {2023}
}

Comments

18 pages, 2 figures