Variations of Mixed Hodge Structure attached to the deformation theory of a Complex Variation of Hodge Structures

Details Variations of Mixed Hodge Structure attached to the deformation theory of a Complex Variation of Hodge Structures Variations of Mixed Hodge Structure attached to the deformation theory of a Complex Variation of Hodge Structures

2009-02-16

arxiv.org/abs/0902.2626v1

Mathematics

Algebraic Geometry

Scientific paper

We construct a Mixed Hodge Structure on the local complete ring of the representation scheme at the holonomy of a VHS on a compact K\"ahler manifold and prove that the corresponding tautological representation is the holonomy of a VMHS. In order to carry out this construction we revisit the well-known work of Goldman and Millson on the deformation theory of representations of K\"ahler groups.

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