Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures

摘要

Let X be a compact K?hler manifold, x ε X be a base point and ρ: π 1(X; x) → GL_N(C) be the monodromy representation of a C-VHS. Building on Goldman-Millson's classical work, we construct a mixed Hodge structure on the complete local ring of the representation variety at ρ and a variation of mixed Hodge structures whose monodromy is the universal deformation of ρ.