Statements (32)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebraic_geometry
Abelian variety Group variety |
| gptkbp:associatedWith |
Algebraic curve
|
| gptkbp:definedIn |
Field over which the curve is defined
|
| gptkbp:dimensions |
genus of the curve
|
| gptkbp:functorialIn |
gptkb:Curve
|
| gptkbp:hasApplication |
gptkb:Moduli_theory
Cryptography Arithmetic geometry |
| gptkbp:hasPoint |
Corresponds to divisor class of degree zero
|
| gptkbp:heldBy |
gptkb:Lie_group
gptkb:Projective_variety Complex torus (over complex numbers) Connected variety Moduli space for line bundles of degree zero Principally polarized abelian variety Smooth variety Quotient of the space of holomorphic 1-forms by the period lattice (over complex numbers) |
| https://www.w3.org/2000/01/rdf-schema#label |
Jacobian variety of a curve
|
| gptkbp:namedAfter |
gptkb:Carl_Gustav_Jacob_Jacobi
|
| gptkbp:parameter |
Degree zero line bundles on the curve
Divisor classes of degree zero |
| gptkbp:relatedTo |
gptkb:Torelli_theorem
gptkb:Picard_group gptkb:Riemann-Roch_theorem Theta divisor |
| gptkbp:structure |
Commutative group
|
| gptkbp:usedIn |
gptkb:Number_theory
gptkb:Algebraic_geometry |
| gptkbp:bfsParent |
gptkb:principally_polarized_Abelian_variety
|
| gptkbp:bfsLayer |
8
|