In mathematics, a Riemann form in the theory of abelian varieties and modular forms, is the following data: * A lattice Λ in a complex vector space Cg. * An alternating bilinear form α from Λ to the integers satisfying the following Riemann bilinear relations: 1. * the real linear extension αR:Cg × Cg→R of α satisfies αR(iv, iw)=αR(v, w) for all (v, w) in Cg × Cg; 2. * the associated hermitian form H(v, w)=αR(iv, w) + iαR(v, w) is positive-definite. (The hermitian form written here is linear in the first variable.) Riemann forms are important because of the following:

Property Value
dbo:abstract
• In mathematics, a Riemann form in the theory of abelian varieties and modular forms, is the following data: * A lattice Λ in a complex vector space Cg. * An alternating bilinear form α from Λ to the integers satisfying the following Riemann bilinear relations: 1. * the real linear extension αR:Cg × Cg→R of α satisfies αR(iv, iw)=αR(v, w) for all (v, w) in Cg × Cg; 2. * the associated hermitian form H(v, w)=αR(iv, w) + iαR(v, w) is positive-definite. (The hermitian form written here is linear in the first variable.) Riemann forms are important because of the following: * The alternatization of the Chern class of any factor of automorphy is a Riemann form. * Conversely, given any Riemann form, we can construct a factor of automorphy such that the alternatization of its Chern class is the given Riemann form. (en)
dbo:wikiPageID
• 8200934 (xsd:integer)
dbo:wikiPageRevisionID
• 711391902 (xsd:integer)
dbp:id
• A/a010220
• T/t092600
dbp:title
• Abelian function
• Theta-function
dct:subject
http://purl.org/linguistics/gold/hypernym
rdf:type
rdfs:comment
• In mathematics, a Riemann form in the theory of abelian varieties and modular forms, is the following data: * A lattice Λ in a complex vector space Cg. * An alternating bilinear form α from Λ to the integers satisfying the following Riemann bilinear relations: 1. * the real linear extension αR:Cg × Cg→R of α satisfies αR(iv, iw)=αR(v, w) for all (v, w) in Cg × Cg; 2. * the associated hermitian form H(v, w)=αR(iv, w) + iαR(v, w) is positive-definite. (The hermitian form written here is linear in the first variable.) Riemann forms are important because of the following: (en)
rdfs:label
• Riemann form (en)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:wikiPageRedirects of
is foaf:primaryTopic of