Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Complex_torus> ?p ?o. }
Showing items 1 to 30 of
30
with 100 items per page.
- Complex_torus abstract "In mathematics, a complex torus is a particular kind of complex manifold M whose underlying smooth manifold is a torus in the usual sense (i.e. the cartesian product of some number N circles). Here N must be the even number 2n, where n is the complex dimension of M.All such complex structures can be obtained as follows: take a lattice Λ in Cn considered as real vector space; then the quotient groupCn/Λis a compact complex manifold. All complex tori, up to isomorphism, are obtained in this way. For n = 1 this is the classical period lattice construction of elliptic curves. For n > 1 Bernhard Riemann found necessary and sufficient conditions for a complex torus to be an algebraic variety; those that are varieties can be embedded into complex projective space, and are the abelian varieties. The actual projective embeddings are complicated (see equations defining abelian varieties) when n > 1, and are really coextensive with the theory of theta-functions of several complex variables (with fixed modulus). There is nothing as simple as the cubic curve description for n = 1. Computer algebra can handle cases for small n reasonably well. By Chow's theorem, no complex torus other than the abelian varieties can 'fit' into projective space.".
- Complex_torus thumbnail Lattice_torsion_points.svg?width=300.
- Complex_torus wikiPageID "3055042".
- Complex_torus wikiPageRevisionID "601324857".
- Complex_torus hasPhotoCollection Complex_torus.
- Complex_torus subject Category:Abelian_varieties.
- Complex_torus subject Category:Complex_manifolds.
- Complex_torus subject Category:Complex_surfaces.
- Complex_torus type Artifact100021939.
- Complex_torus type ComplexManifolds.
- Complex_torus type Conduit103089014.
- Complex_torus type Manifold103717750.
- Complex_torus type Object100002684.
- Complex_torus type Passage103895293.
- Complex_torus type PhysicalEntity100001930.
- Complex_torus type Pipe103944672.
- Complex_torus type Tube104493505.
- Complex_torus type Way104564698.
- Complex_torus type Whole100003553.
- Complex_torus type YagoGeoEntity.
- Complex_torus type YagoPermanentlyLocatedEntity.
- Complex_torus comment "In mathematics, a complex torus is a particular kind of complex manifold M whose underlying smooth manifold is a torus in the usual sense (i.e. the cartesian product of some number N circles). Here N must be the even number 2n, where n is the complex dimension of M.All such complex structures can be obtained as follows: take a lattice Λ in Cn considered as real vector space; then the quotient groupCn/Λis a compact complex manifold. All complex tori, up to isomorphism, are obtained in this way.".
- Complex_torus label "Complex torus".
- Complex_torus sameAs m.08nhq6.
- Complex_torus sameAs Q5156610.
- Complex_torus sameAs Q5156610.
- Complex_torus sameAs Complex_torus.
- Complex_torus wasDerivedFrom Complex_torus?oldid=601324857.
- Complex_torus depiction Lattice_torsion_points.svg.
- Complex_torus isPrimaryTopicOf Complex_torus.
