  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 $\mathbb{P}^n$.
