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In mathematics, a theta characteristic of a non-singular algebraic curve C is a divisor class Θ such that 2Θ is the canonical class. In terms of holomorphic line bundles L on a connected compact Riemann surface, it is therefore L such that L2 is the canonical bundle, here also equivalently the holomorphic cotangent bundle. In terms of algebraic geometry, the equivalent definition is as an invertible sheaf, which squares to the sheaf of differentials of the first kind. Theta characteristics were introduced by Rosenhain

Attributes	Values
rdf:type	yago:WikicatThetaFunctions yago:Abstraction100002137 yago:Attribute100024264 yago:Curve113867641 yago:Function113783816 yago:Line113863771 yago:MathematicalRelation113783581 yago:Relation100031921 yago:Shape100027807 yago:WikicatAlgebraicCurves
rdfs:label	세타 지표 (ko) Theta characteristic (en)
rdfs:comment	In mathematics, a theta characteristic of a non-singular algebraic curve C is a divisor class Θ such that 2Θ is the canonical class. In terms of holomorphic line bundles L on a connected compact Riemann surface, it is therefore L such that L2 is the canonical bundle, here also equivalently the holomorphic cotangent bundle. In terms of algebraic geometry, the equivalent definition is as an invertible sheaf, which squares to the sheaf of differentials of the first kind. Theta characteristics were introduced by Rosenhain (en) 대수기하학에서 세타 지표(θ指標, 영어: theta characteristic)는 대수 곡선의 표준 선다발의 제곱근이다. 리만 곡면의 경우, 이는 스핀 구조에 해당한다. (ko)
dcterms:subject	Theta functions Algebraic curves
Wikipage page ID	7193470 (xsd:integer)
Wikipage revision ID	1079903128 (xsd:integer)
Link from a Wikipage to another Wikipage	Non-singular Arf invariant Invertible sheaf Jacobian variety Coset Mathematics Elliptic curve Theta function Complex torus Theta functions Algebraic curve Algebraic geometry Quadratic form Hasse-Witt matrix Intersection form (4-manifold) Abelian variety Algebraic curves Characteristic 2 Bitangent Bitangents of a quartic Circle group Dolgachev Canonical bundle Compact Riemann surface Weil pairing Divisor class group Canonical class Spin structure P-rank of an abelian variety Divisor class Quartic curve Differentials of the first kind Holomorphic cotangent bundle Holomorphic line bundle Jacobian elliptic function
Link from a Wikipage to an external page	http://www.numdam.org/item%3Fid=ASENS_1971_4_4_1_47_0 http://www.numdam.org/item%3Fid=ASENS_1971_4_4_2_181_0 http://www.math.lsa.umich.edu/~idolga/lecturenotes.html
sameAs	Theta characteristic Theta characteristic Theta characteristic Theta characteristic Theta characteristic
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harvtxt dbt:Harvs
has abstract	In mathematics, a theta characteristic of a non-singular algebraic curve C is a divisor class Θ such that 2Θ is the canonical class. In terms of holomorphic line bundles L on a connected compact Riemann surface, it is therefore L such that L2 is the canonical bundle, here also equivalently the holomorphic cotangent bundle. In terms of algebraic geometry, the equivalent definition is as an invertible sheaf, which squares to the sheaf of differentials of the first kind. Theta characteristics were introduced by Rosenhain (en) 대수기하학에서 세타 지표(θ指標, 영어: theta characteristic)는 대수 곡선의 표준 선다발의 제곱근이다. 리만 곡면의 경우, 이는 스핀 구조에 해당한다. (ko)
gold:hypernym	Θ
prov:wasDerivedFrom	wikipedia-en:Theta_characteristic?oldid=1079903128&ns=0
page length (characters) of wiki page	5144 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Theta_characteristic
is Link from a Wikipage to another Wikipage of	Johann Georg Rosenhain Equations defining abelian varieties Bitangents of a quartic Spin structure
is foaf:primaryTopic of	wikipedia-en:Theta_characteristic

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