Let be a compact Kähler manifold, be a base point and be the monodromy representation of a -VHS. Building on Goldman–Millson’s classical work, we construct a mixed Hodge structure on the complete local ring of the representation variety at and a variation of mixed Hodge structures whose monodromy is the universal deformation of .
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Philippe Eyssidieux, Carlos Simpson, Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures. J. Eur. Math. Soc. 13 (2011), no. 6, pp. 1769–1798DOI 10.4171/JEMS/293