Logarithmic form

In contexts including complex manifolds and algebraic geometry, a logarithmic differential form is a meromorphic differential form with poles of a certain kind. The concept was introduced by Deligne.

Let X be a complex manifold, and D ⊂ X a divisor and ω a holomorphic p-form on X−D. If ω and dω have a pole of order at most one along D, then ω is said to have a logarithmic pole along D. ω is also known as a logarithmic p-form. The logarithmic p-forms make up a subsheaf of the meromorphic p-forms on X with a pole along D, denoted