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- Logarithmic_form abstract "In contexts including complex manifolds and algebraic geometry, a logarithmic differential form is a meromorphic differential form with poles of a certain kind.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, denotedIn the theory of Riemann surfaces, one encounters logarithmic one-forms which have the local expressionfor some meromorphic function (resp. rational function) , where g is holomorphic and non-vanishing at 0, and m is the order of f at 0.. That is, for some open covering, there are local representations of this differential form as a logarithmic derivative (modified slightly with the exterior derivative d in place of the usual differential operator d/dz). Observe that ω has only simple poles with integer residues. On higher-dimensional complex manifolds, the Poincaré residue is used to describe the distinctive behavior of logarithmic forms along poles.".
- Logarithmic_form wikiPageID "1052096".
- Logarithmic_form wikiPageRevisionID "603808756".
- Logarithmic_form hasPhotoCollection Logarithmic_form.
- Logarithmic_form subject Category:Algebraic_geometry.
- Logarithmic_form subject Category:Complex_analysis.
- Logarithmic_form comment "In contexts including complex manifolds and algebraic geometry, a logarithmic differential form is a meromorphic differential form with poles of a certain kind.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.".
- Logarithmic_form label "Logarithmic form".
- Logarithmic_form sameAs m.041syr.
- Logarithmic_form sameAs Q6667308.
- Logarithmic_form sameAs Q6667308.
- Logarithmic_form wasDerivedFrom Logarithmic_form?oldid=603808756.
- Logarithmic_form isPrimaryTopicOf Logarithmic_form.