Techniques of constructions of variations of mixed Hodge structures

TL;DR

This paper introduces a method to construct real variations of mixed Hodge structures on compact Kähler manifolds using Sullivan's minimal models and associated differential graded algebras.

Contribution

It provides a novel approach to constructing mixed Hodge structures leveraging Sullivan's 1-minimal models and differential graded algebra techniques.

Findings

Constructs real variations of mixed Hodge structures on compact Kähler manifolds.

Uses mixed Hodge structures on Sullivan's 1-minimal models.

Establishes a new framework connecting differential graded algebras with Hodge theory.

Abstract

We give a way of constructing real variations of mixed Hodge structures over compact K\"ahler manifolds by using mixed Hodge structures on Sullivan's $1$-minimal models of certain differential graded algebras associated with real variations of Hodge structures.