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Gauss-Manin system and mixed Hodge structure. (English) Zbl 0516.32012


MSC:

32J25 Transcendental methods of algebraic geometry (complex-analytic aspects)
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
32S05 Local complex singularities
14B07 Deformations of singularities
58A14 Hodge theory in global analysis
32Sxx Complex singularities

Citations:

Zbl 0278.14003
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References:

[1] Brieskorn, E.: Die Monodromie der isolierten Singular itaten von Hyperflachen. Manuscripta Math., 2, 103-161 (1970). · Zbl 0186.26101 · doi:10.1007/BF01155695
[2] Brylinski, J. L.: Modules holonomes a singularites regulieres et filtration de Hodge, I (preprint). · Zbl 0598.14008
[3] Deligne, P.: Equations differentielles a points singuliers reguliers. Lect. Notes in Math., vol. 163, Springer (1970). · Zbl 0244.14004 · doi:10.1007/BFb0061194
[4] Pham, F.: Singularites des systemes differentiels de Gauss-Manin. Progress in Math., 2, Birkhauser (1979). · Zbl 0524.32015
[5] Saito, M.: On the exponents and the geometric genus of an isolated hypersurface singularity (to appear in Proceedings of the Symposia in pure Math., 40, A.M.S.). · Zbl 0545.14031
[6] Scherk, J.: A note on two local Hodge filtrations (to appear). · Zbl 0533.14003
[7] Scherk, J., and Steenbrink, J.: On the mixed Hodge structure on the coho-mology of the Milnor fiber (preprint). · Zbl 0618.14002 · doi:10.1007/BF01456138
[8] Schmid, W.: Variation of Hodge structure: the singularities of the period mapping. Invent, math., 22, 211-319 (1973). · Zbl 0278.14003 · doi:10.1007/BF01389674
[9] Steenbrink, J. H. M.: Mixed Hodge structure on the vanishing cohomology. Proceedings of the Nordic Summer School, Oslo, pp. 525-563 (1976). · Zbl 0373.14007
[10] Varchenko, A.: Asymptotics of holomorphic forms define mixed Hodge structure. Dokl. Akad. Nauk. SSSR, 255(5), 1035-1038 (1980). · Zbl 0516.14007
[11] Varchenko, A.: Asymptotic mixed Hodge structure on vanishing cohomology. Izv. Akad. Nauk. SSSR, Ser. Math., 45(3), 540-591 (1981). · Zbl 0476.14002
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