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Claude Sabbah
Non-commutative Hodge structures
(Structures de Hodge non commutatives)
Annales de l'institut Fourier, 61 no. 7 (2011), p. 2681-2717, doi: 10.5802/aif.2790
Article PDF | Reviews MR 3112504 | Zbl pre06193023
Class. Math.: 14D07, 34M40
Keywords: Non-commutative Hodge structure, Fourier-Laplace transformation, Brieskorn lattice

Résumé - Abstract

This article gives a survey of recent results on a generalization of the notion of a Hodge structure. The main example is related to the Fourier-Laplace transform of a variation of polarizable Hodge structure on the punctured affine line, like the Gauss-Manin systems of a proper or tame algebraic function on a smooth quasi-projective variety. Variations of non-commutative Hodge structures often occur on the tangent bundle of Frobenius manifolds, giving rise to a tt* geometry.

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