##  [Abel-Jacobi Map](/index.php/abel-jacobi-map) 

  ##  [Abel-Jacobi Map](https://algebra.quantumdictionary.io/abel-jacobi-map-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A map sending algebraic cycle classes that are homologically trivial to points in an analytic complex torus (an intermediate Jacobian or Jacobian), constructed by integrating appropriate differential forms along chains bounding the cycle; for curves it sends degree-zero divisors to the Jacobian via integration of holomorphic differentials.