Formal Abel-Jacobi maps

TL;DR

This paper develops a general framework for the infinitesimal Abel-Jacobi map using formal deformation theory and differential graded Lie algebras, extending classical concepts.

Contribution

It introduces a homotopy-theoretic approach to the infinitesimal Abel-Jacobi map within a broad formal deformation setting.

Findings

Realizes the infinitesimal Abel-Jacobi map as a morphism in the homotopy category of dg Lie algebras.

Provides a general construction encompassing the classical Abel-Jacobi map.

Establishes a formal deformation theory perspective for Abel-Jacobi maps.

Abstract

We realize the infinitesimal Abel-Jacobi map as a morphism of formal deformation theories, realized as a morphism in the homotopy category of differential graded Lie algebras. The whole construction is carried out in a general setting, of which the classical Abel-Jacobi map is a special example.