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

Source abstract

Let X be a compact Kähler manifold, x\in X be a base point and \rho: \pi_1(X,x) \to GL_N(\mathbb C) be the monodromy representation of a \mathbb 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 \rho and a variation of mixed Hodge structures whose monodromy is the universal deformation of \rho .