Sheaf of principal parts of germs of meromorphic functions

Definition

The sheaf of principal parts of germs of meromorphic functions on a complex manifold is defined as the quotient sheaf of the sheaf of meromorphic functions by the sheaf of holomorphic functions (both viewed as sheaves of Abelian groups).

A section of this sheaf over a subset of the manifold is termed a system of principal parts. Cousin's additive problem asks whether, given a system of principal parts, there exists a meromorphic function in a neighborhood of that subset, that yields precisely those principal parts.