Griffiths, P. A. Periods of integrals on algebraic manifolds. III: Some global differential-geometric properties of the period mapping. (English) Zbl 0212.53503 Publ. Math., Inst. Hautes Étud. Sci. 38, 125-180 (1970). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 125 Documents MSC: 14D07 Variation of Hodge structures (algebro-geometric aspects) 14C30 Transcendental methods, Hodge theory (algebro-geometric aspects) Citations:Zbl 0169.52303; Zbl 0183.25501 PDFBibTeX XMLCite \textit{P. A. Griffiths}, Publ. Math., Inst. Hautes Étud. Sci. 38, 125--180 (1970; Zbl 0212.53503) Full Text: DOI Numdam EuDML References: [1] M. F. Atiyah, The signature of fibre-bundles,Global Analysis (papers in honor of K. Kodaira), Princeton Univ. Press (1969), 73–89. [2] A. Blanchard, Sur les variétés analytiques complexes,Ann. Sci. École Norm. Sup.,73 (1956), 157–202. · Zbl 0073.37503 [3] S. Bochner andK. Yano,Curvature and Betti Numbers, Princeton Univ. Press, 1953. [4] A. Borel andHarish-Chandra, Arithmetic subgroups of algebraic groups,Ann. of Math.,75 (1962), 485–535. · Zbl 0107.14804 · doi:10.2307/1970210 [5] A. Borel andR. Narasimhan, Uniqueness conditions for certain holomorphic mappings,Invent. Math.,2 (1966), 247–255. · Zbl 0145.31802 · doi:10.1007/BF01425403 [6] E. Cartan,Leçons sur la géométrie des espaces de Riemann, Paris, Gauthier-Villars, 1951. · Zbl 0044.18401 [7] S. S. Chern, On holomorphic mappings of Hermitian manifolds of the same dimension,Proc. Symp. in Pure Math.,11, American Mathematical Society, 1968. · Zbl 0184.31202 [8] S. S. Chern, Characteristic classes of Hermitian manifolds,Ann. of Math.,47 (1946), 85–121. · Zbl 0060.41416 · doi:10.2307/1969037 [9] P. Deligne, Théorie de Hodge, to appear inPubl. I.H.E.S. [10] H. Grauert, Über Modifikationen und exzeptionelle analytische Mengen,Math. Annalen,146 (1962), 331–368. · Zbl 0173.33004 · doi:10.1007/BF01441136 [11] P. A. Griffiths, Periods of integrals on algebraic manifolds, I and II,Amer. Jour. Math.,90 (1968), 568–626 and 805–865. · Zbl 0169.52303 · doi:10.2307/2373545 [12] P. A. Griffiths,Monodromy of homology and periods of integrals on algebraic manifolds, lecture notes available from Princeton University, 1968. [13] P. A. Griffiths, Periods of integrals on algebraic manifolds,Bull. Amer. Math. Soc.,75 (1970), 228–296. · Zbl 0214.19802 · doi:10.1090/S0002-9904-1970-12444-2 [14] P. A. Griffiths, Some results on algebraic cycles on algebraic manifolds,Algebraic Geometry (papers presented at Bombay Colloquium), Oxford University Press, 1969, 93–191. [15] P. A. Griffiths, Periods of certain rational integrals,Ann. of Math.,90 (1969), 460–541. · Zbl 0215.08103 · doi:10.2307/1970746 [16] P. A. Griffiths andW. Schmid, Locally homogeneous complex manifolds,Acta Math.,123 (1970), 253–302. · Zbl 0209.25701 · doi:10.1007/BF02392390 [17] A. Grothendieck, Un théorème sur les homomorphismes de schémas abéliens,Invent. Math.,2 (1966), 59–78. · Zbl 0147.20302 · doi:10.1007/BF01403390 [18] A. Grothendieck, On the de Rham cohomology of albebraic varieties,Publ. Math. I.H.E.S.,29 (1966), 95–103. · Zbl 0145.17602 [19] R. Gunning andH. Rossi,Analytic Functions of Several Variables, Prentice-Hall, 1965. · Zbl 0141.08601 [20] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, I and II,Ann. of Math.,79 (1964), 109–326. · Zbl 0122.38603 · doi:10.2307/1970486 [21] F. Hirzebruch,Neue Topologische Methoden in der Algebraischen Geometrie, Springer-Verlag, 1956. · Zbl 0074.36701 [22] W. V. D. Hodge,The Theory and Applications of Harmonic Integrals, Cambridge University Press, 1959. · Zbl 0104.40902 [23] J. King,Families of intermediate Jacobians, thesis at University of California, Berkeley, 1969. [24] K. Kodaira andD. C. Spencer, On deformations of complex analytic structures, I and II,Ann. of Math.,67 (1958), 328–466. · Zbl 0128.16901 · doi:10.2307/1970009 [25] M. H. Kwack, Generalization of the big Picard theorem,Ann. of Math.,90 (1969), 13–22. · Zbl 0179.12103 · doi:10.2307/1970678 [26] S. Lefschetz,L’Analysis Situs et la Géométrie Algébrique, Paris, Gautheir-Villars, 1924. [27] D. Lieberman, Higher Picard varieties,Amer. Jour. Math.,90 (1968), 1165–1199. · Zbl 0183.25401 · doi:10.2307/2373295 [28] G. Mostow andT. Tamagawa, On the compactness of arithmetically defined homogeneous spaces,Am. of Math.,76 (1962), 446–463. · Zbl 0196.53201 · doi:10.2307/1970368 [29] C. L. Siegel,Analytic functions of several complex variables, lecture notes from Institute for Advanced Study, Princeton, 1962. [30] A. Weil,Variétés Kähleriennes, Paris, Hermann, 1958. This reference list is based on information provided by the publisher or from digital mathematics libraries. 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