Abelianness of the “missing part” from a sheaf category to a module category

Abstract

This paper investigates the structure of the “missing part” from the category of coherent sheaves over a weighted projective line of weight type (2, 2, n) to the category of finitely generated right modules on the associated canonical algebra. By constructing a t-structure in the stable category of the vector bundle category, we show that the “missing part” is equivalent to the heart of the t-structure, hence it is abelian. Moreover, it is equivalent to the category of finitely generated modules on the path algebra of type $\mathbb{A}_{n - 1}$.