Non-commutative Hodge structures

Claude Sabbah[1]

  • [1] École polytechnique Centre de Mathématiques Laurent Schwartz UMR 7640 du CNRS F–91128 Palaiseau cedex (France)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 7, page 2681-2717
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Sabbah, Claude. "Non-commutative Hodge structures." Annales de l’institut Fourier 61.7 (2011): 2681-2717. <http://eudml.org/doc/275636>.

@article{Sabbah2011,
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.},
affiliation = {École polytechnique Centre de Mathématiques Laurent Schwartz UMR 7640 du CNRS F–91128 Palaiseau cedex (France)},
author = {Sabbah, Claude},
journal = {Annales de l’institut Fourier},
keywords = {Non-commutative Hodge structure; Fourier-Laplace transformation; Brieskorn lattice; non-commutative Hodge structure},
language = {eng},
number = {7},
pages = {2681-2717},
publisher = {Association des Annales de l’institut Fourier},
title = {Non-commutative Hodge structures},
url = {http://eudml.org/doc/275636},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Sabbah, Claude
TI - Non-commutative Hodge structures
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 7
SP - 2681
EP - 2717
AB - 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.
LA - eng
KW - Non-commutative Hodge structure; Fourier-Laplace transformation; Brieskorn lattice; non-commutative Hodge structure
UR - http://eudml.org/doc/275636
ER -

References

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