Source: wikibot/abel-jacobi-map
= Abel–Jacobi map
{wiki=Abel–Jacobi_map}
The Abel-Jacobi map is a fundamental concept in algebraic geometry and the theory of algebraic curves. It connects the geometric properties of curves with their Abelian varieties, particularly in the context of the study of divisors on a curve. \#\#\# Definition and Context 1. **Algebraic Curves**: Consider a smooth projective algebraic curve \\( C \\) over an algebraically closed field \\( k \\).