- Jacobian variety
In

mathematics , the**Jacobian variety**of a non-singularalgebraic curve "C" of genus "g ≥ 1" is a particularabelian variety "J", ofdimension "g". The curve "C" is asubvariety of "J", and generates "J" as a group.Analytically, it can be realized as the

quotient space "V"/"L", where "V" is thevector space of all:$l\; =\; int\_\{gamma\}\; (cdot):\; \{mbox\{rational\; differentials\; on\; \}\; C\; mbox\{\; without\; poles\}\}\; longrightarrow\; mathbb\{C\},\; quad\; omega\; mapsto\; int\_\{gamma\}\; omega$

where "γ" is a path in "C(

**C**)", and "L" is the lattice of all those "l" with closed path "γ".An important

theorem regarding Jacobian varieties is Abel's theorem.**References***

*cite conference | author=J.S. Milne | title=Jacobian Varieties | booktitle=Arithmetic Geometry |publisher=Springer-Verlag|location=New York| year=1986 | pages=pp. 167-212|id=ISBN 0-387-96311-1

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