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Vanishing Theorems for Resolutions of Surfaces Singularities.

Jonathan M. Wahl (1976)

Inventiones mathematicae

Variation of mixed Hodge structures arising from family of logarithmic deformations

Sampei Usui (1983)

Annales scientifiques de l'École Normale Supérieure

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

Philippe Eyssidieux, Carlos Simpson (2011)

Journal of the European Mathematical Society

Let $X$ be a compact Kähler manifold, $x \in X$ be a base point and $ρ : π_{1} (X, x) \to G L_{N} (C)$ 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 $ρ$ .