Factorization of the Abel-Jacobi maps

TL;DR

This paper provides a direct proof that the Abel-Jacobi map factors through another regular homomorphism, utilizing Lawson homology and morphic cohomology theories.

Contribution

It offers a straightforward proof of Walker's theorem on the factorization of the Abel-Jacobi map, simplifying previous approaches.

Findings

Confirmed the factorization of the Abel-Jacobi map using a direct proof.

Connected Lawson homology and morphic cohomology in the context of Abel-Jacobi maps.

Enhanced understanding of the structure of Abel-Jacobi maps in algebraic geometry.

Abstract

As an application of the theory of Lawson homology and morphic cohomology, Walker proved that the Abel-Jacobi map factors through another regular homomorphism. In this note, we give a direct proof of the theorem.