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

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...

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Veröffentlicht in:	Journal of the European Mathematical Society : JEMS 2011-01, Vol.13 (6), p.1769-1798
Hauptverfasser:	Eyssidieux, Philippe, Simpson, Carlos
Format:	Artikel
Sprache:	eng
Schlagworte:	Differential geometry
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creator	Eyssidieux, Philippe Simpson, Carlos
description	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 $\rho$ .
doi_str_mv	10.4171/JEMS/293
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title	Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures
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