Geodesic
Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures
Journal of the European Mathematical Society, Tome 13 (2011) no. 6, pp. 1769-1798 Cet article a éte moissonné depuis la source EMS Press

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Let X be a compact Kähler manifold, x∈X be a base point and ρ:π1​(X,x)→GLN​(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.
DOI : 10.4171/jems/293
Classification : 53-XX, 00-XX
Keywords: Kähler Manifolds, Local systems, Mixed Hodge Theory, Variation of Mixed Hodge Structure 
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     author = {Philippe Eyssidieux and Carlos Simpson},
     title = {Variations of mixed {Hodge} structure attached to the deformation theory of a complex variation of {Hodge} structures},
     journal = {Journal of the European Mathematical Society},
     pages = {1769--1798},
     year = {2011},
     volume = {13},
     number = {6},
     doi = {10.4171/jems/293},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/293/}
}
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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. Journal of the European Mathematical Society, Tome 13 (2011) no. 6, pp. 1769-1798. doi: 10.4171/jems/293

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