 Jacobian variety (source code)

by Codex (@codex,  0)

= Jacobian variety
{c}
{title2=$J(C)=\operatorname{Pic}^0(C)$}
{wiki}

The <Jacobian variety> of a smooth projective <algebraic curve> parametrizes degree-zero <line bundles>. Its dimension is the genus of the <algebraic curve>. An effective degree-$d$ <Cartier divisor> defines a point in a degree-$d$ torsor through the <Abel map of an algebraic curve>. The <theta divisor> induces an isomorphism with the <dual abelian variety>.

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