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Jacobian variety
In mathematics, the Jacobian variety ''J(C)'' of a non-singular algebraic curve ''C'' of genus ''g'' is the moduli space of degree 0 line bundles. It is the connected component of the identity in the Picard group of ''C'', hence an abelian variety.
==Introduction==
The Jacobian variety is named after Carl Gustav Jacobi, who proved the complete version Abel-Jacobi theorem, making the injectivity statement of Niels Abel into an isomorphism. It is a principally polarized abelian variety, of dimension ''g'', and hence, over the complex numbers, it is a complex torus. If ''p'' is a point of ''C'', then the curve ''C'' can be mapped to a subvariety of ''J'' with the given point ''p'' mapping to the identity of ''J'', and ''C'' generates ''J'' as a group.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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