English

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

Algebraic Geometry 2011-01-04 v2 Complex Variables

Abstract

We associate to any convenient nondegenerate Laurent polynomial 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 the Laurent polynomial (or its universal unfolding) and of the corresponding Hodge theory.

Cite

@article{arxiv.math/0211352,
  title  = {Gauss-Manin systems, Brieskorn lattices and Frobenius structures (I)},
  author = {Antoine Douai and Claude Sabbah},
  journal= {arXiv preprint arXiv:math/0211352},
  year   = {2011}
}

Comments

52 pages, 2 figures, LaTeX + smf classes available at http://smf.emath.fr/Publications/Formats/index.html typos corrected, remarks added at the end of the introduction, in sect. 3, and a new appendix added. to appear in Ann. Institut Fourier (Grenoble)