The Hodge theoretic fundamental group and its cohomology

2009/02/24 by Donu Arapura, Arapura, Donu
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0902.4252

openalex publication_date 2009/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we explore a notion of nonabelian Hodge structure on the fundamental group of an algebraic variety. This is approach is compared to some alternative approaches due to Morgan, Hain and others. We also give criteria for a variety to be a Hodge theoretic K(pi,1), which roughly means that the cohomology of variations of mixed Hodge structure can be determined from the group.

Related

• Mixed Hodge structures and representations of fundamental groups of\n algebraic varieties
• Nonabelian mixed Hodge structures
• Mixed Hodge Structures
• Hodge number polynomials for nearby and vanishing cohomology
• Local Mixed Hodge Structure on Brill-Noether Stacks