Periods of integrals on algebraic manifolds: Summary of main results and discussion of open problems
Phillip A. Griffiths
Source: Bull. Amer. Math. Soc. Volume 76, Number 2
(1970), 228-296.
First Page:
Show
Hide
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.bams/1183531477
Mathematical Reviews number (MathSciNet): MR0258824
Zentralblatt MATH identifier: 0214.19802
References
1. P. Deligne, Théorie de Hodge (to appear). (Cf. Deligne's article Théorème de Lefschetz et critères de dégénérescence de suites spectrales, Inst. Hautes Etudes Sci. Publ. Math. No. 35 (1968), 107-126.)
Zentralblatt MATH: 0159.22501
Mathematical Reviews (MathSciNet): MR244265
2. P. Griffiths, Periods of integrals on algebraic manifolds. I, II, Amer. J. Math. 90 (1968), 568-626; 805-865. MR 37 #5215; MR 38 #2146.
Zentralblatt MATH: 0183.25501
3. P. Griffiths, On the periods of integrals on algebraic manifolds, Rice Univ. Studies 54 (1968), 21-38.
Zentralblatt MATH: 0188.24801
Mathematical Reviews (MathSciNet): MR242844
4. P. Griffiths and W. Schmid, Locally homogeneous complex manifolds, Acta Math, (to appear).
Zentralblatt MATH: 0209.25701
Mathematical Reviews (MathSciNet): MR259958
Digital Object Identifier: doi:10.1007/BF02392390
5. A. Grothendieck, On the de Rham cohomology of algebraic varieties, Inst. Hautes Études Sci. Publ. Math. No. 29 (1966), 95-103. MR 33 #7343.
Zentralblatt MATH: 0145.17602
Mathematical Reviews (MathSciNet): MR199194
Digital Object Identifier: doi:10.1007/BF02684807
6. W. V. D. Hodge, The theory and applications of harmonic integrals, 2nd ed., Cambridge Univ. Press, New York, 1952. MR 14, 500.
Zentralblatt MATH: 0024.39703
Mathematical Reviews (MathSciNet): MR51571
7. S. Lefschetz, L'analysis situs et la géométrie algébrique, Gauthier-Villars, Paris, 1924.
8. J. Milnor, Singular points of complex hypersurfaces, Ann. of Math. Studies, no. 61, Princeton Univ. Press, Princeton, N. J., 1968.
Zentralblatt MATH: 0184.48405
Mathematical Reviews (MathSciNet): MR239612
9. A. Weil, Introduction à l'étude des variétés kählériennes, Publ. Inst. Math. Nancago, no. VI, Actualités Sci. Indust., no. 1267, Hermann, Paris, 1958. MR 22 #1921.
Zentralblatt MATH: 0141.19202
Mathematical Reviews (MathSciNet): MR111056
10. W. L. Baily, Jr. and A. Borel, Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math. (2) 84 (1966), 442-528. MR 35 #6870.
Zentralblatt MATH: 0154.08602
Mathematical Reviews (MathSciNet): MR216035
Digital Object Identifier: doi:10.2307/1970457
11. A. Borel and R. Narasimhan, Uniqueness conditions for certain holomorphic mappings, Invent. Math. 2 (1967), 247-255. MR 35 #414.
Zentralblatt MATH: 0145.31802
Mathematical Reviews (MathSciNet): MR209517
Digital Object Identifier: doi:10.1007/BF01425403
12. S. S. Chern, Characteristic classes of Hermitian manifolds, Ann. of Math. (2) 47 (1946), 85-121. MR 7, 470.
Zentralblatt MATH: 0060.41416
Mathematical Reviews (MathSciNet): MR15793
Digital Object Identifier: doi:10.2307/1969037
13. S. S. Chern, On holomorphic mappings of Hermitian manifolds of the same dimension, Proc. Sympos. Pure Math., vol. 11, Amer. Math. Soc., Providence, R. I., 1968, pp. 157-170. MR 38 #2714.
Zentralblatt MATH: 0184.31202
Mathematical Reviews (MathSciNet): MR234397
14. C. H. Clemens, Jr., Picard-Lefschetz theorem for families of nonsingular algebraic varieties acquiring ordinary singularities, Trans. Amer. Math. Soc. 136 (1969), 93-108. MR 38 #2135.
Zentralblatt MATH: 0185.51302
Mathematical Reviews (MathSciNet): MR233814
Digital Object Identifier: doi:10.1090/S0002-9947-1969-0233814-9
15. P. Deligne, Monograph on connexions with regular singular points, Springer-Verlag (to appear).
Mathematical Reviews (MathSciNet): MR1857369
Zentralblatt MATH: 1040.14006
Digital Object Identifier: doi:10.1007/PL00004499
16. P. Griffiths, Monodromy of homology and periods of integrals on algebraic manifolds, preprint from Princeton University, Princeton, N.J.
Mathematical Reviews (MathSciNet): MR242844
Zentralblatt MATH: 0188.24801
17. P. Griffiths, A theorem on periods of integrals on algebraic manifolds, Rice Univ. Studies (to appear).
Zentralblatt MATH: 0224.14006
Mathematical Reviews (MathSciNet): MR242844
18. A. Grothendieck, Un théorème sur les homomorphismes de schémas abéliens, Invent. Math. 2 (1966), 59-78. MR 36 #180.
Zentralblatt MATH: 0147.20302
Mathematical Reviews (MathSciNet): MR217089
Digital Object Identifier: doi:10.1007/BF01403390
19. P. Deligne and A. Grothendieck, S. G. A. 7 (on monodromy theorems), Inst. Hautes Études Sci. Publ. Math. (1968/70).
Mathematical Reviews (MathSciNet): MR1640253
20. K. Kodaira, On compact analytic surfaces. III, Ann. of Math. (2) 78 (1963), 1-40. MR 32 #1730.
Zentralblatt MATH: 0171.19601
Mathematical Reviews (MathSciNet): MR184257
Digital Object Identifier: doi:10.2307/1970500
21. K. Kodaira, On characteristic systems of families of surfaces with ordinary singularities in a projective space, Amer. J. Math. 87 (1965), 227-256. MR 31 #652.
Zentralblatt MATH: 0145.43802
Mathematical Reviews (MathSciNet): MR176380
Digital Object Identifier: doi:10.2307/2373235
22. A. Landman, On the Picard-Lefschetz transformations. Thesis, University of California, Berkeley, Calif., 1966.
23. D. Lieberman, Higher Picard varieties, Amer. J. Math. 90 (1968), 1165-1199.
Zentralblatt MATH: 0183.25401
Mathematical Reviews (MathSciNet): MR238857
Digital Object Identifier: doi:10.2307/2373295
24. W. Schmid, On a conjecture of Langlands, Ann. of Math, (to appear).
Zentralblatt MATH: 0291.43013
Mathematical Reviews (MathSciNet): MR286942
Digital Object Identifier: doi:10.2307/1970751
25. Séminaire H. Cartan, Fonctions automorphes, 10e Année, 1957/58, Secrétariat mathématique, Paris, 1958. MR 21 #2750.
26. H. Wu, Normal families of holomorphic mappings, Acta Math. 119 (1967), 193-233. MR 37 #468.
Zentralblatt MATH: 0158.33301
Mathematical Reviews (MathSciNet): MR224869
Digital Object Identifier: doi:10.1007/BF02392083
Bulletin of the American Mathematical Society
