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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, 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

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rdfs:label	Logarithmic form (en) 対数的微分形式 (ja)
rdfs:comment	複素多様体論や代数多様体論では、対数的(logarithmic)微分形式は、ある種類の極をもつ有理型微分形式である。 X を複素多様体とし、D ⊂ X を因子、ω を X−D 上の正則 p-形式とする。ω と dω が D に沿って大きくとも 1 の位数の極を持つとき、ω を D に沿って対数的極を持つという。ω は対数的 p-形式とも呼ばれる。対数的 p-形式はD に沿った X 上の有理 p-形式の層をなし、次のように書く。リーマン面の理論では、次の局所表現を持つ対数的 1-形式が存在する。ある有理型函数（有理函数）に対しとなる。ここに g は 0 で正則で 0 とはならなく、m は f の 0 でのオーダーである。すなわち、ある開被覆が存在し、この微分形式の対数微分としての局所表現が存在する（通常の微分作用素 d/dz の中の外微分 d を少し変形する）。ω が整数の留数の単純極を持つだけであることに注意する。高次元の複素多様体では、(Poincaré residue)は、極に沿った対数的微分形式の振る舞いを記述することに使われる。 (ja) 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, 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 (en)
dcterms:subject	Complex analysis Algebraic geometry
Wikipage page ID	1052096 (xsd:integer)
Wikipage revision ID	1031079913 (xsd:integer)
Link from a Wikipage to another Wikipage	Projective space Meromorphic function Holomorphic function Elliptic function Poincaré residue Complex manifold Pole (complex analysis) Adjunction formula Logarithmic derivative Algebraic geometry Exterior derivative Differential of the first kind Differential operator Gysin sequence Projective variety Rational function Hypersurface Riemann surfaces Complex analysis Algebraic geometry Hodge theory Differential form Picard group Borel–Moore homology Pierre Deligne Dolbeault isomorphism Open covering Sheaf (mathematics) Exact sequence Sheaf cohomology Smooth scheme Normal crossings Residue Theorem Hypercohomology Differentials of the first kind dbr:Residue_map
Link from a Wikipage to an external page	http://math.columbia.edu/~dejong/seminar/note_on_algebraic_de_Rham_cohomology.pdf
sameAs	Logarithmic form Logarithmic form Logarithmic form Logarithmic form
dbp:wikiPageUsesTemplate	dbt:Reflist
has abstract	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, 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 In the theory of Riemann surfaces, one encounters logarithmic one-forms which have the local expression for 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. (en) 複素多様体論や代数多様体論では、対数的(logarithmic)微分形式は、ある種類の極をもつ有理型微分形式である。 X を複素多様体とし、D ⊂ X を因子、ω を X−D 上の正則 p-形式とする。ω と dω が D に沿って大きくとも 1 の位数の極を持つとき、ω を D に沿って対数的極を持つという。ω は対数的 p-形式とも呼ばれる。対数的 p-形式はD に沿った X 上の有理 p-形式の層をなし、次のように書く。リーマン面の理論では、次の局所表現を持つ対数的 1-形式が存在する。ある有理型函数（有理函数）に対しとなる。ここに g は 0 で正則で 0 とはならなく、m は f の 0 でのオーダーである。すなわち、ある開被覆が存在し、この微分形式の対数微分としての局所表現が存在する（通常の微分作用素 d/dz の中の外微分 d を少し変形する）。ω が整数の留数の単純極を持つだけであることに注意する。高次元の複素多様体では、(Poincaré residue)は、極に沿った対数的微分形式の振る舞いを記述することに使われる。 (ja)
prov:wasDerivedFrom	wikipedia-en:Logarithmic_form?oldid=1031079913&ns=0
page length (characters) of wiki page	9326 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Logarithmic_form
is Link from a Wikipage to another Wikipage of	Residue theorem Index of logarithm articles Jacobian ideal Generalized continued fraction Logarithm Adjunction formula Dolbeault cohomology Log structure Alan Baker (mathematician) Differential of the first kind Hyperhomology Hodge structure Pierre Deligne Gysin homomorphism
is foaf:primaryTopic of	wikipedia-en:Logarithmic_form

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