Degenerating variations of Hodge structure

Cattani, Eduardo ; Kaplan, Aroldo

Théorie de Hodge - Luminy, Juin 1987, Astérisque, no. 179-180 (1989), pp. 67-96.

MR Zbl

@incollection{AST_1989__179-180__67_0,
     author = {Cattani, Eduardo and Kaplan, Aroldo},
     title = {Degenerating variations of {Hodge} structure},
     booktitle = {Th\'eorie de Hodge - Luminy, Juin 1987},
     editor = {Barlet D. and Esnault H. and Elzein F. and Verdier Jean-Louis and Viehweg E.},
     series = {Ast\'erisque},
     pages = {67--96},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {179-180},
     year = {1989},
     mrnumber = {1042802},
     zbl = {0705.14006},
     language = {en},
     url = {http://www.numdam.org/item/AST_1989__179-180__67_0/}
}

TY  - CHAP
AU  - Cattani, Eduardo
AU  - Kaplan, Aroldo
TI  - Degenerating variations of Hodge structure
BT  - Théorie de Hodge - Luminy, Juin 1987
AU  - Collectif
ED  - Barlet D.
ED  - Esnault H.
ED  - Elzein F.
ED  - Verdier Jean-Louis
ED  - Viehweg E.
T3  - Astérisque
PY  - 1989
SP  - 67
EP  - 96
IS  - 179-180
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_1989__179-180__67_0/
LA  - en
ID  - AST_1989__179-180__67_0
ER  -

%0 Book Section
%A Cattani, Eduardo
%A Kaplan, Aroldo
%T Degenerating variations of Hodge structure
%B Théorie de Hodge - Luminy, Juin 1987
%A Collectif
%E Barlet D.
%E Esnault H.
%E Elzein F.
%E Verdier Jean-Louis
%E Viehweg E.
%S Astérisque
%D 1989
%P 67-96
%N 179-180
%I Société mathématique de France
%U http://www.numdam.org/item/AST_1989__179-180__67_0/
%G en
%F AST_1989__179-180__67_0

Cattani, Eduardo; Kaplan, Aroldo. Degenerating variations of Hodge structure, dans Théorie de Hodge - Luminy, Juin 1987, Astérisque, no. 179-180 (1989), pp. 67-96. http://www.numdam.org/item/AST_1989__179-180__67_0/

Bibliographie
Cité par

[1] E. Cattani and A. Kaplan: Polarized mixed Hodge structures and the local monodromy of a variation of Hodge structure. Invent. Math. 67, 101-115 (1982). | DOI | EuDML | MR | Zbl

[2] E. Cattani and A. Kaplan: On the $S L (2)$ -orbits in Hodge Theory. IHES pre-pub. /M/82/58. October 1982.

[3] E. Cattani and A. Kaplan: Sur la cohomologie $L_{2}$ et la cohomologie d' intersection à coefficients dans une variation de structure de Hodge. C. R. Acad. Sci. Paris, Série I, 300, 351-353 (1985). | MR | Zbl

[4] E. Cattani, A. Kaplan and W. Schmid: Degeneration of Hodge structures. Ann. of Math., 123, 457-535 (1986). | DOI | MR | Zbl

[5] E. Cattani, A. Kaplan and W. Schmid: $L^{2}$ and intersection cohomologies for a polarizable variation of Hodge structure. Invent. Math. 87, 217-252 (1987). | DOI | EuDML | MR | Zbl

[6] E. Cattani, A. Kaplan and W. Schmid: Variations of polarized Hodge structure: asymptotics and monodromy. In: Hodge Theory, Lecture Notes in Math. 1246, Springer-Verlag, 16-31 (1987). | DOI | MR | Zbl

[7] E. Cattani, A. Kaplan and W. Schmid: Some remarks on $L^{2}$ and intersection cohomologies. In: Hodge Theory, Lecture Notes in Math. 1246, Springer-Verlag, 32-41 (1987). | DOI | MR | Zbl

[8] C. H. Clemens, Degeneration of Kähler manifolds, Duke Math. J. 44, 215-290 (1977). | DOI | MR | Zbl

[9] M. Cornalba and P. Griffiths, Some transcendental aspects of algebraic geometry. In: Proceedings of Symposia in Pure Mathematics, Vol. 29, A.M.S., 3-110 (1975). | DOI | MR | Zbl

[10] M. Cornalba and P. Griffiths: Analytic cycles and vector bundles on non-compact algebraic varieties. Invent. Math. 28, 1-106 (1975). | DOI | EuDML | MR | Zbl

[11] P. Deligne: Équations différentielles à points singuliers réguliers. Lecture Notes in Math. 163, Springer-Verlag (1970). | MR | Zbl

[12] P. Deligne: La conjecture de Weil, II. Publ. Math. I.H.E.S. 52, 137-252 (1980). | DOI | EuDML | Numdam | MR | Zbl

[13] P. Deligne: Structures de Hodge mixtes réelles. Appendix to [2]. | DOI | Zbl

[14] F. Elzein: Théorie de Hodge à coefficients dégénérescents. - These proceedings.

[15] P. Griffiths : Periods of integrals on algebraic manifolds, I, Amer. J. Math. 90, 568-626 (1968). | DOI | MR | Zbl

P. Griffiths : Periods of integrals on algebraic manifolds, II. Amer. J. Math. 90, 805-865 (1968). | DOI | Zbl

P. Griffiths : Periods of integrals on algebraic manifolds, III, Publ. Math. I.H.E.S. 38, 125-180 (1970). | DOI | EuDML | Numdam | Zbl

[16] P. Griffiths, ed.: Topics in Transcendental Algebraic Geometry, Annals of Mathematics Studies 106, Princeton U. Press, (1984). | MR | Zbl

[17] P. Griffiths and W. Schmid: Locally homogeneous complex manifolds, Acta Math. 123, 253-302 (1969). | DOI | MR | Zbl

[18] P. Griffiths and W. Schmid: Recent developments in Hodge theory: a discussion of techniques and results. In: Discrete Subgroups of Lie Groups and Applications to Moduli, Oxford University Press (1973). | MR | Zbl

[19] M. Kashiwara: The asymptotic behavior of a variation of polarized Hodge structure. Publ. RIMS, Kyoto Univ., 21, 853-875 (1985). | DOI | MR | Zbl

[20] M. Kashiwara: A study of variation of mixed Hodge structure. Publ. RIMS, Kyoto Univ. 22, 991-1024 (1986). | DOI | MR | Zbl

[21] M. Kashiwara and T. Kawai: Hodge structure and holonomic systems. Proc. Japan Acad., 62, 1-4 (1986). | DOI | MR | Zbl

[22] M. Kashiwara and T. Kawai: The Poincaré Lemma for variations of polarized Hodge structure. Publ. RIMS, Kyoto Univ., 23, 345-407 (1987). | DOI | MR | Zbl

[23] N. Katz: Nilpotent connections and the monodromy theorem; Applications of a result of Turritin. Publ. Math. I.H.E.S. 39, 175-232 (1970). | DOI | EuDML | Numdam | MR | Zbl

[24] J. Kollár: Subadditivity of the Kodaira dimension: fibers of general type. In: Adv. Studies in Pure Math. 10, Algebraic Geometry, Sendai, 1985, 361-398 (1987). | DOI | MR | Zbl

[25] A. Landman: On the Picard-Lefschetz transformation for algebraic manifolds acquiring general singularities, Trans. A.M.S. 181, 89-126 (1973). | DOI | MR | Zbl

[26] C. Peters: A criterion for flatness of Hodge bundles over curves and geometric applications. Math. Ann. 268, 1-19 (1984). | DOI | EuDML | MR | Zbl

[27] M. Saito: Article in these Proceedings.

[28] W. Schmid: Variation of Hodge structure: The singularities of the period mapping, Invent. Math. 22, 211-319 (1973). | DOI | EuDML | MR | Zbl

[29] W. Schmid: Abbildungen in arithmetische Quotienten hermitesch symmetrischer Räume, In: Lect. Notes in Math. 412, Springer-Verlag, 211-319, (1974). | MR | Zbl

[30] J. Steenbrink: Limits of Hodge structures, Invent. Math. 31, 229-257 (1976). | DOI | EuDML | MR | Zbl

[31] S. Zucker: Hodge theory with degenerating coefficients: $L_{2}$ -cohomology in the Poincaré metric, Ann. of Math. 109 415-476 (1979). | DOI | MR | Zbl

[32] S. Zucker: Remarks on a theorem of Fujita, J. Math. Soc. Japan 34, 47-54 (1982). | DOI | MR | Zbl