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Polarized mixed Hodge structures and the local monodromy of a variation of Hodge structure. (English) Zbl 0516.14005


MSC:

14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
32J25 Transcendental methods of algebraic geometry (complex-analytic aspects)

Citations:

Zbl 0456.14014

References:

[1] Cattani, E., Kaplan, A.: The monodromy weight filtration for a several variables degeneration of Hodge structures of weight two. Inventiones Math.52, 131-142 (1979) · Zbl 0408.32005 · doi:10.1007/BF01403060
[2] Cattani, E., Kaplan, A.: On the local monodromy of a variation of Hodge structure. Bull. Amer. Math. Soc.4, 116-118 (1981) · Zbl 0472.14007 · doi:10.1090/S0273-0979-1981-14876-X
[3] Deligne, P.: Théorie de Hodge, II. Publ. Math. I.H.E.S.40, 5-57 (1972) · Zbl 0219.14007
[4] Deligne, P.: La conjecture de Weil, II. Publ. Math. I.H.E.S.52, 137-252 (1980) · Zbl 0456.14014
[5] Griffiths, P.A.: Periods of integrals on algebraic manifolds, I, II. Amer. J. Math.90, 568-626; 805-865 (1968) · Zbl 0169.52303 · doi:10.2307/2373545
[6] Griffiths, P.A.: Periods of integrals on algebraic manifolds: summary of main results and discussion of open problems. Bull. Amer. Math. Soc.76, 228-296 (1970) · Zbl 0214.19802 · doi:10.1090/S0002-9904-1970-12444-2
[7] Griffiths, P.A., Schmid, W.: Recent developments in Hodge Theory: a discussion of techniques and results. Proceedings of the International Colloquium on Discrete Subgroups of Lie Groups, pp. 31-127, Bombay 1973; Oxford Univ. Press, 1975
[8] Kostant, B.: The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group. Amer. J. Math.81, 973-1032 (1959) · Zbl 0099.25603 · doi:10.2307/2372999
[9] Schmid, B.: Variation of Hodge structure: the singularities of the period mapping. Inventiones Math.22, 211-319 (1973) · Zbl 0278.14003 · doi:10.1007/BF01389674
[10] Serre, J.P.: Cohomologie Galoisienne. Lecture Notes Math. Vol.5, Berlin: Springer 1973 · Zbl 0259.12011
[11] Steenbrink, J.: Limits of Hodge structures. Inventiones Math.31, 229-257 (1976) · doi:10.1007/BF01403146
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