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- Torelli_theorem abstract "In mathematics, the Torelli theorem is a classical result of algebraic geometry over the complex number field, stating that a non-singular projective algebraic curve (compact Riemann surface) C is determined by its Jacobian variety J(C), when the latter is given in the form of a principally polarized abelian variety. In other words the complex torus J(C), with certain 'markings', is enough to recover C. The same statement holds over any algebraically closed field. From more precise information on the constructed isomorphism of the curves it follows that if the canonically principally polarized Jacobian varieties of curves of genus are k-isomorphic for k any perfect field, so are the curves.This result has had many important extensions. It can be recast to read that a certain natural morphism, the period mapping, from the moduli space of curves of a fixed genus, to a moduli space of abelian varieties, is injective (on geometric points). Generalizations are in two directions. Firstly, to geometric questions about that morphism, for example the local Torelli theorem. Secondly, to other period mappings. A case that has been investigated deeply is for K3 surfaces.".
- Torelli_theorem wikiPageID "3002552".
- Torelli_theorem wikiPageRevisionID "590296032".
- Torelli_theorem hasPhotoCollection Torelli_theorem.
- Torelli_theorem subject Category:Abelian_varieties.
- Torelli_theorem subject Category:Algebraic_curves.
- Torelli_theorem subject Category:Moduli_theory.
- Torelli_theorem subject Category:Theorems_in_algebraic_geometry.
- Torelli_theorem subject Category:Theorems_in_complex_geometry.
- Torelli_theorem type AbelianVarieties.
- Torelli_theorem type Abstraction100002137.
- Torelli_theorem type AlgebraicCurves.
- Torelli_theorem type Assortment108398773.
- Torelli_theorem type Attribute100024264.
- Torelli_theorem type Collection107951464.
- Torelli_theorem type Communication100033020.
- Torelli_theorem type Curve113867641.
- Torelli_theorem type Group100031264.
- Torelli_theorem type Line113863771.
- Torelli_theorem type Message106598915.
- Torelli_theorem type Proposition106750804.
- Torelli_theorem type Shape100027807.
- Torelli_theorem type Statement106722453.
- Torelli_theorem type Theorem106752293.
- Torelli_theorem type TheoremsInAlgebraicGeometry.
- Torelli_theorem type TheoremsInComplexGeometry.
- Torelli_theorem comment "In mathematics, the Torelli theorem is a classical result of algebraic geometry over the complex number field, stating that a non-singular projective algebraic curve (compact Riemann surface) C is determined by its Jacobian variety J(C), when the latter is given in the form of a principally polarized abelian variety. In other words the complex torus J(C), with certain 'markings', is enough to recover C. The same statement holds over any algebraically closed field.".
- Torelli_theorem label "Torelli theorem".
- Torelli_theorem sameAs 토렐리_정리.
- Torelli_theorem sameAs m.08jx2f.
- Torelli_theorem sameAs Q7825663.
- Torelli_theorem sameAs Q7825663.
- Torelli_theorem sameAs Torelli_theorem.
- Torelli_theorem wasDerivedFrom Torelli_theorem?oldid=590296032.
- Torelli_theorem isPrimaryTopicOf Torelli_theorem.