Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)

Antoine Douai[1]; Claude Sabbah[2]

  • [1] Université de Nice, Laboratoire J.A. Dieudonné, UMR 6621 du CNRS, Parc Valrose, 06108 Nice Cedex 2 (France)
  • [2] École Polytechnique, Centre de mathématiques, 91128 Palaiseau Cedex (France)

Annales de l’institut Fourier (2003)

  • Volume: 53, Issue: 4, page 1055-1116
  • ISSN: 0373-0956

Abstract

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We associate to any convenient nondegenerate Laurent polynomial f on the complex torus ( ℂ * ) n a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of f (or its universal unfolding) and of the corresponding Hodge theory.

How to cite

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Douai, Antoine, and Sabbah, Claude. "Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)." Annales de l’institut Fourier 53.4 (2003): 1055-1116. <http://eudml.org/doc/116062>.

@article{Douai2003,
abstract = {We associate to any convenient nondegenerate Laurent polynomial $f$ on the complex torus $(\{\mathbb \{C\}\}^*)^n$ a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of $f$ (or its universal unfolding) and of the corresponding Hodge theory.},
affiliation = {Université de Nice, Laboratoire J.A. Dieudonné, UMR 6621 du CNRS, Parc Valrose, 06108 Nice Cedex 2 (France); École Polytechnique, Centre de mathématiques, 91128 Palaiseau Cedex (France)},
author = {Douai, Antoine, Sabbah, Claude},
journal = {Annales de l’institut Fourier},
keywords = {Gauss-Manin system; Brieskorn lattice; Frobenius manifold; D-modules; Brieskorn lattices},
language = {eng},
number = {4},
pages = {1055-1116},
publisher = {Association des Annales de l'Institut Fourier},
title = {Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)},
url = {http://eudml.org/doc/116062},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Douai, Antoine
AU - Sabbah, Claude
TI - Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)
JO - Annales de l’institut Fourier
PY - 2003
PB - Association des Annales de l'Institut Fourier
VL - 53
IS - 4
SP - 1055
EP - 1116
AB - We associate to any convenient nondegenerate Laurent polynomial $f$ on the complex torus $({\mathbb {C}}^*)^n$ a canonical Frobenius-Saito structure on the base space of its universal unfolding. According to the method of K. Saito (primitive forms) and of M. Saito (good basis of the Gauss-Manin system), the main problem, which is solved in this article, is the analysis of the Gauss-Manin system of $f$ (or its universal unfolding) and of the corresponding Hodge theory.
LA - eng
KW - Gauss-Manin system; Brieskorn lattice; Frobenius manifold; D-modules; Brieskorn lattices
UR - http://eudml.org/doc/116062
ER -

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