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・ Jacobi rotation
・ Jacobi set
・ Jacobi sum
・ Jacobi symbol
・ Jacobi theta functions (notational variations)
・ Jacobi triple product
・ Jacobi zeta function
・ Jacobi's formula
・ Jacobi's four-square theorem
・ Jacobi's theorem
・ Jacobian
・ Jacobian conjecture
・ Jacobian curve
・ Jacobian ideal
・ Jacobian matrix and determinant
Jacobian variety
・ Jacobiasca formosana
・ Jacobie Adriaanse
・ Jacobikerk
・ Jacobin
・ Jacobin (disambiguation)
・ Jacobin (hummingbird)
・ Jacobin (magazine)
・ Jacobin (pigeon)
・ Jacobin (politics)
・ Jacobin Club of Mysore
・ Jacobin cuckoo
・ Jacobin novel
・ Jacobina
・ Jacobina do Piauí


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Jacobian variety : ウィキペディア英語版
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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