JournalsjemsVol. 13, No. 6pp. 1769–1798

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

  • Philippe Eyssidieux

    Université Joseph Fourier, Grenoble, Saint-Martin-d'Hères, France
  • Carlos Simpson

    Université de Nice Sophia Antipolis, France
Variations of mixed Hodge structure attached to the deformation theory of a complex variation of Hodge structures cover
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Abstract

Let XX be a compact Kähler manifold, xXx\in X be a base point and  ρ:π1(X,x)GLN(C)\rho: \pi_1(X,x) \to GL_N(\mathbb C) be the monodromy representation of a C\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 ρ\rho and a variation of mixed Hodge structures whose monodromy is the universal deformation of ρ\rho.

Cite this article

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. 1769–1798

DOI 10.4171/JEMS/293