Morgan's mixed Hodge structures and nonabelian Hodge structures

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.

22 pages The paper have been shorten for journal submission purposes. Some contents in the previous version have been removed

References in corpus (4)

• Deformation theory via differential graded Lie algebras
• E_1-Formality of Complex Algebraic Varieties
• The Hodge theoretic fundamental group and its cohomology
• Deformations of representations of fundamental groups of complex varieties