Generalized intermediate Jacobians and the theorem on normal functions. (English) Zbl 0329.14008


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)
32L05 Holomorphic bundles and generalizations
14F25 Classical real and complex (co)homology in algebraic geometry
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[1] Andreotti, A., Frankel, T.: The second Lefschetz Theorem on hyperplane sections. In: Global Analysis, pp. 1-20. Princeton: Princeton University Press 1969 · Zbl 0191.19301
[2] Bloch, S., Griffiths, P.: A theorem about normal functions associated to Lefschetz pencils on algebraic varieties. Manuscript, Princeton University (1971)
[3] Brieskorn, E.: Beispiele zur Differentialtopologie von Singularitäten. Inventiones math.2, 1-14 (1966) · Zbl 0145.17804 · doi:10.1007/BF01403388
[4] Clemens, C., Griffiths, P.: The intermediate Jacobian of the cubic threefold. Annals of Math.95(2), 281-356 (1972) · doi:10.2307/1970801
[5] Deligne, P.: Théorème de Lefschetz et critères de dégénérescence de suites spectrales. Pub. Math. I.H.E.S.35, 107-126 (1969) · Zbl 0159.22501
[6] Deligne, P.: Equations différentielles à points singuliers réguliers. In: Lecture Notes in Math. 163. Berlin-Heidelberg-New York: Springer 1970 · Zbl 0244.14004
[7] Deligne, P.: Théorie de Hodge, II. Pub. Math. I.H.E.S.40, 5-57 (1971) · Zbl 0219.14007
[8] Federer, H.: Geometric measure theory. Berlin-Heidelberg-New York: Springer 1969 · Zbl 0176.00801
[9] Godement, R.: Topologie algébrique et théorie des faisceaux. Paris: Hermann 1964
[10] Grauert, H.: Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strukturen. Pub. Math. I.H.E.S.5 (1960) · Zbl 0158.32901
[11] Greenberg, M.: Lectures on algebraic topology. New York: Benjamin 1967 · Zbl 0169.54403
[12] Griffiths, P.: On the periods of certain rational integrals: I and II. Annals of Math.90(3), 460-541 (1969) · Zbl 0215.08103 · doi:10.2307/1970746
[13] Griffiths, P.: On the periods of certain rational integrals: III. Manuscript, Princeton University (1969) · Zbl 0215.08103
[14] Griffiths, P.: Periods of integrals on algebraic manifolds, III. Pub. Math. I.H.E.S.38, 125-180 (1970) · Zbl 0212.53503
[15] Griffiths, P.: Periods of integrals on algebraic manifolds: Summary of main results and discussion of open problems. Bull. AMS76(2), 228-296 (1970) · Zbl 0214.19802 · doi:10.1090/S0002-9904-1970-12444-2
[16] Griffiths, P., Schmid, W.: Recent developments in Hodge Theory. Proceedings of the International Colloquium on Discrete Subgroups of Lie Groups and Applications to Moduli, Bombay, January 1973. Bombay: Oxford University Press 1975
[17] Grothendieck, A.: Sur la classification des fibrés holomorphes sur la sphere de Riemann. Amer. J. Math.79, 121-138 (1957) · Zbl 0079.17001 · doi:10.2307/2372388
[18] Grothendieck, A.: Eléments de géométrie algébrique III (première partie). Pub. Math. I.H.E.S.11 (1961)
[19] Grothendieck, A.: Eléments de géométrie algébrique III (seconde partie). Pub. Math. I.H.E.S.17 (1963)
[20] Katz, N.: The regularity theorem in algebraic geometry. Actes, Congrès Intern. Math.1, 437-443 (1970)
[21] Katz, N.: Etude cohomologique des pinceaux de Lefschetz. SGA 7, Exposé XVIII
[22] Katz, N., Oda, T.: On the differentiation of de Rham cohomology classes with respect to parameters. J. Math. Kyoto Univ. 8-2, 199-213 (1968) · Zbl 0165.54802
[23] Kodaira, K., Morrow, J.: Complex manifolds. New York: Holt, Rinehart and Winston 1971 · Zbl 0325.32001
[24] Landman, A.: On the Picard-Lefschetz transformation for algebraic manifolds acquiring general singularities. Trans AMS181, 89-126 (1973) · Zbl 0284.14005 · doi:10.1090/S0002-9947-1973-0344248-1
[25] Lefschetz, S.: L’analysis situs et la géométrie algébrique. Paris: Gauthier-Villars 1924
[26] Lojasiewicz, S.: Triangulation of semi-analytic sets. Annali Scuola Norm. Sup. Pisa18, 449-474 (1964) · Zbl 0128.17101
[27] Mumford, D.: Abelian varieties. Bombay: Oxford University Press 1970 · Zbl 0223.14022
[28] Rham, G. de: Variétés différentiables, 3rd ed. Paris: Hermann 1960
[29] Schmid, W.: Variation of Hodge structure: The singularities of the period mapping. Inventiones math.22, 211-319 (1973) · Zbl 0278.14003 · doi:10.1007/BF01389674
[30] Serre, J-P.: Geométrie algébrique et géométrie analytique. Annales l’Inst. Fourier6, 1-42 (1955-6)
[31] Steenbrink, J.: Limits of Hodge structures and intermediate Jacobians. Thesis, University of Amsterdam, 1974 · Zbl 0329.14007
[32] Steenbrink, J.: A note on Lefschetz Pencils, manuscript, 1974
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