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A study of variation of mixed Hodge structure. (English) Zbl 0621.14007
By an admissible graded polarizable variation of mixed Hodge structure (g.p. VMHS) on a complex space X (on which a smooth Zariski open subset \(X^*\) is given) the author understands a g.p. VMHS whose restriction to any curve meeting \(X^*\) is admissible in the sense of J. Steenbrink and S. Zucker [Invent. Math. 80, 489-542 (1985)]. A study of admissible g.p. VMHS’ is made; especially it is proved that if admissibility holds outside a subspace of codimension 2 of X then it holds on the whole of X (provided X is smooth and \(X\setminus X^*\) is a divisor with normal crossings).
Reviewer: A.Buium

MSC:
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
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[1] E. Cattani and A. Kaplan, Polarized mixed Hodge structures and the local monodromy of a variation of Hodge structure, Inv. Math., 67 (1982), 101-115. · Zbl 0516.14005 · doi:10.1007/BF01393374 · eudml:142901
[2] E. Cattani, A. Kaplan and W. Schmid, 1. Degeneration of Hodge structures, preprint. 2. L2 and intersection cohomologies for a polarizable variation of Hodge structures, preprint. · Zbl 0611.14006
[3] P. Deligne, Theorie de Hodge I, II, III, Actes Congres Intern, math. 1970, 425-430; Publ. Math. I. H. E. S., 40 (1971), 5-58; 44 (1974), 5-77.
[4] A. Galligo, M. Granger and Ph. Maisonobe, D-modules et faisceaux pervers dont le support singulier est un croisement normal, to appear in Ann. Sci. EC. Norm. Sup. · Zbl 0572.32013
[5] M. Kashiwara, The asymptotic behavior of a variation of polarized Hodge structure, Publ. RIMS, Kyoto Univ., 21 (1985), 853-875. · Zbl 0594.14012 · doi:10.2977/prims/1195178935
[6] M. Kashiwara, and T. Kawai, 1 . The Poincare lemma for a variation of polarized Hodge structure, preprint RIMS- 540, the announcement is appeared in Proc. Japan Acad., 61, Ser. A (1985), 164-167. · Zbl 0576.14010 · doi:10.3792/pjaa.61.164
[7] W. Schmid, Variation of Hodge structure ; the singularities of the period mapping, Inv. Math., 22 (1973), 211-319. · Zbl 0278.14003 · doi:10.1007/BF01389674 · eudml:142246
[8] J. Steenbrink and S. Zucker, Variation of mixed Hodge structure I, Inv. Math,. 80 (1985), 485-542. · Zbl 0626.14007 · doi:10.1007/BF01388729 · eudml:143242
[9] S. Zucker, Variation of mixed Hodge structure II, Inv. Math., 80 (1985), 543-565. · Zbl 0615.14003 · doi:10.1007/BF01388730 · eudml:143243
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