The Hodge theoretic fundamental group and its cohomology

Details The Hodge theoretic fundamental group and its cohomology The Hodge theoretic fundamental group and its cohomology

2009-02-24

arxiv.org/abs/0902.4252v2

Mathematics

Algebraic Geometry

19 pages, final revision, to appear in Proc. Alg. Cycles Conf. Ohio State

Scientific paper

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.

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