Morgan's mixed Hodge structures and nonabelian Hodge structures

TL;DR

This paper refines Morgan's mixed Hodge structures using non-abelian Hodge theory and provides explicit representatives of real unipotent variations on compact Kähler manifolds.

Contribution

It introduces a new approach combining Morgan's work with non-abelian Hodge theory to explicitly represent variations of mixed Hodge structures.

Findings

Refined Morgan's mixed Hodge structures with non-abelian Hodge theory

Explicit representatives of real unipotent variations on Kähler manifolds

Enhanced understanding of Hodge structures in complex geometry

Abstract

We refine the Morgan's work on mixed Hodge structures on Sullivan's $1$--minimal models by using non-abelian Hodge theory. As an application, we give explicit representatives of real unipotent variations of mixed Hodge structures over compact K"ahler manifolds.