Jacobian variety of a curve

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:Group_variety gptkb:algebraic_geometry gptkb:Abelian_variety
gptkbp:associatedWith	gptkb: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)
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
https://www.w3.org/2000/01/rdf-schema#label	Jacobian variety of a curve