On exact sequences of Hodge theoretic fundamental groups

2025/03/17 by Xu, Simon Shuofeng
#14D07 #14H10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.13307

Abstract

The goal of this paper is to first define a Hodge theoretic fundamental group for smooth connected complex algebraic varieties and then prove and study a right exact sequence of Hodge theoretic fundamental groups associated to a smooth projective family of algebraic varieties f\colon X→ B. In particular, we study when this right exact sequence is exact, relate this question to some prior results in non-abelian Hodge theory, and give an obstruction to splitting in terms of étale fundamental groups. The main examples we consider in this note is the universal curve f\colon C_g→ M_g and the moduli space of degree 1 line bundles on the universal curves p \colon Pic¹_Cg/Mg→ M_g.

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