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In contexts including [[complex manifold]]s and [[algebraic geometry]], a '''logarithmic''' [[differential form]] is a meromorphic differential form with [[pole]]s{{dn|date=November 2012}} of a certain kind.
Let ''X'' be a complex manifold, and <math> D\subset X </math> a [[divisor]] and <math>\omega </math> a holomorphic ''p''-form on <math>X-D </math>. If <math>\omega</math> and <math>d\omega</math> have a pole of order at most one along ''D'', then <math>\omega</math> is said to have a logarithmic pole along ''D''. <math>\omega</math> is also known as a logarithmic ''p''-form. The logarithmic ''p''-forms make up a [[Sheaf_(mathematics)|subsheaf]] of the meromorphic ''p''-forms on ''X'' with a pole along ''D'', denoted <math>\Omega^p_X(\log D)</math>.
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