A map from Lawson homology to Deligne Cohomology

TL;DR

This paper constructs a natural map from Lawson homology to Deligne cohomology for smooth complex projective varieties using Harvey-Lawson spark complexes, and compares it to existing Abel-Jacobi type constructions.

Contribution

It introduces a new natural map connecting Lawson homology and Deligne cohomology, enhancing understanding of their relationship in algebraic geometry.

Findings

Established a map from Lawson homology to Deligne cohomology

Compared the new map with Abel-Jacobi type constructions

Provided insights into the relationship between these cohomological theories

Abstract

A natural map from Lawson homology to Deligne cohomology groups for smooth complex projective varieties is constructed by using the Harvey-Lawson spark complexes. We also compare this to Abel-Jacobi type constructions by others.