Gauss - Manin Systems , Brieskorn Lattices and Frobenius Structures ( I )
نویسندگان
چکیده
— 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. Résumé (Systèmes de Gauss-Manin, réseaux de Brieskorn et structures de Frobenius (I)) Nous associons à tout polynôme de Laurent commode et non dégénéré f par rapport à son polyèdre de Newton sur le tore complexe (C∗ )n une structure de Frobenius-Saito canonique sur la base de son déploiement universel. En suivant la méthode de K. Saito (formes primitives) et de M. Saito (bonnes bases du système de Gauss-Manin), le problème principal, qui est résolu dans cet article, consiste en l’analyse du système de Gauss-Manin de f (ou de son déploiement universel) et de la théorie de Hodge correspondante. Antoine Douai, UMR 6621 du CNRS, Laboratoire J.A. Dieudonné, Université de Nice, Parc Valrose, 06108 Nice cedex 2, France • E-mail : [email protected] Claude Sabbah, UMR 7640 du CNRS, Centre de Mathématiques, École polytechnique, F–91128 Palaiseau cedex, France • E-mail : [email protected] Url : http://www.math.polytechnique.fr/cmat/sabbah/sabbah.html 2000 Mathematics Subject Classification. — 32S40, 32S30, 32G34, 32G20, 34Mxx.
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ar X iv : m at h / 02 11 35 2 v 2 [ m at h . A G ] 8 A pr 2 00 3 GAUSS - MANIN SYSTEMS , BRIESKORN LATTICES AND FROBENIUS STRUCTURES
— We associate to any convenient nondegenerate Laurent polynomial f on the complex torus (C) 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 univ...
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