×
King, James R.

Global residues and intersections on a complex manifold. (English) Zbl 0301.32005

Trans. Am. Math. Soc. 192, 163-199 (1974).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0301.32005

Cited in 1 Review
Cited in 7 Documents

MSC:

32A25 Integral representations; canonical kernels (Szegő, Bergman, etc.)
32G20 Period matrices, variation of Hodge structure; degenerations
58A25 Currents in global analysis
32C30 Integration on analytic sets and spaces, currents
32C35 Analytic sheaves and cohomology groups
Cite Review PDF
Full Text: DOI

References:

[1] Paul F. Baum and Raoul Bott, On the zeros of meromorphic vector-fields, Essays on Topology and Related Topics (Mémoires dédiés à Georges de Rham), Springer, New York, 1970, pp. 29 – 47. · Zbl 0193.52201
[2] Thomas Bloom and Miguel Herrera, De Rham cohomology of an analytic space, Invent. Math. 7 (1969), 275 – 296. · Zbl 0175.37301 · doi:10.1007/BF01425536
[3] Armand Borel and André Haefliger, La classe d’homologie fondamentale d’un espace analytique, Bull. Soc. Math. France 89 (1961), 461 – 513 (French). · Zbl 0102.38502
[4] Glen E. Bredon, Sheaf theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. · Zbl 0158.20505
[5] Michael J. Cowen, Hermitian vector bundles and value distribution for Schubert cycles, Trans. Amer. Math. Soc. 180 (1973), 189 – 228. · Zbl 0277.32018
[6] Pierre Dolbeault, Formes différentielles et cohomologie sur une variété analytique complexe. I, Ann. of Math. (2) 64 (1956), 83 – 130 (French). · Zbl 0072.40603 · doi:10.2307/1969950
[7] Richard N. Draper, Intersection theory in analytic geometry, Math. Ann. 180 (1969), 175 – 204. · Zbl 0157.40502 · doi:10.1007/BF01350737
[8] Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969. · Zbl 0176.00801
[9] Roger Godement, Topologie algébrique et théorie des faisceaux, Actualit’es Sci. Ind. No. 1252. Publ. Math. Univ. Strasbourg. No. 13, Hermann, Paris, 1958 (French). · Zbl 0080.16201
[10] Phillip A. Griffiths, Some results on algebraic cycles on algebraic manifolds, Algebraic Geometry (Internat. Colloq., Tata Inst. Fund. Res., Bombay, 1968), Oxford Univ. Press, London, 1969, pp. 93 – 191.
[11] Robin Hartshorne, Local cohomology, A seminar given by A. Grothendieck, Harvard University, Fall, vol. 1961, Springer-Verlag, Berlin-New York, 1967. · Zbl 0237.14008
[12] Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. · Zbl 0141.08601
[13] M. Herrera, Résidus multiples sur les espaces complexes, Journées complexes: équations différentielles et fonctions de plusieurs variables (Metz, 1972) Inst. Recherche Math. Avancée, Strasbourg, 1973, pp. i+10 (French).
[14] M. Herrera and D. Lieberman, Residues and principal values on complex spaces, Math. Ann. 194 (1971), 259 – 294. · Zbl 0224.32012 · doi:10.1007/BF01350129
[15] Heisuke Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109 – 203; ibid. (2) 79 (1964), 205 – 326. · Zbl 0122.38603
[16] F. Hirzebruch, Neue topologische Methoden in der algebraischen Geometrie, Ergebnisse der Mathematik und ihrer Grenzgebiete (N.F.), Heft 9, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1956 (German). · Zbl 0101.38301
[17] Ludger Kaup, Eine Künnethformel für Fréchetgarben, Math. Z. 97 (1967), 158 – 168 (German). · Zbl 0191.53701 · doi:10.1007/BF01111357
[18] James R. King, A residue formula for complex subvarieties, Proc. Carolina Conf. on Holomorphic Mappings and Minimal Surfaces (Chapel Hill, N.C., 1970) Dept. of Math., Univ. of North Carolina, Chapel Hill, N.C., 1970, pp. 43 – 56. · Zbl 0224.32009
[19] James R. King, The currents defined by analytic varieties, Acta Math. 127 (1971), no. 3-4, 185 – 220. · Zbl 0224.32008 · doi:10.1007/BF02392053
[20] -, The Abel-Jacobi map for families of Kähler manifolds (to appear).
[21] Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol. I, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1996. Reprint of the 1963 original; A Wiley-Interscience Publication. Shoshichi Kobayashi and Katsumi Nomizu, Foundations of differential geometry. Vol. II, Wiley Classics Library, John Wiley & Sons, Inc., New York, 1996. Reprint of the 1969 original; A Wiley-Interscience Publication.
[22] P. Lelong, Fonctionnelles analytiques et fonctions entières, Université de Montréal, 1967. · Zbl 0194.38801
[23] -, Fonctions plurisousharmoniques et formes différentielles positives, Gordon and Breach, New York; distributed by Dunod, Paris, 1969. MR 39 #4436.
[24] -, Séminaire Pierre Lelong, 1970, Springer-Verlag, New York, 1971.
[25] Raghavan Narasimhan, Compact analytical varieties, Enseignement Math. (2) 14 (1968), 75 – 98. · Zbl 0164.09502
[26] François Norguet, Introduction à la théorie cohomologique des résidus, Séminaire Pierre Lelong (Analyse) (année 1970), Springer, Berlin, 1971, pp. 34 – 55. Lecture Notes in Math., Vol. 205 (French).
[27] Jean-Baptiste Poly, Sur un théorème de J. Leray en théorie des résidus, C. R. Acad. Sci. Paris Sér. A-B 274 (1972), A171 – A174 (French). · Zbl 0226.32005
[28] G. de Rham, Variétés différentiables. Formes, courants, formes harmoniques, Actualités Sci. Indust., no. 1222, Hermann. Paris, 1955. MR 16, 957. · Zbl 0065.32401
[29] Laurent Schwartz, Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. IX-X. Nouvelle édition, entiérement corrigée, refondue et augmentée, Hermann, Paris, 1966 (French). · Zbl 0962.46025
[30] Wilhelm Stoll, Value distribution of holomorphic maps into compact complex manifolds., Lecture Notes in Mathematics, Vol. 135, Springer-Verlag, Berlin-New York, 1970. · Zbl 0195.36702
[31] Gabriel Stolzenberg, Volumes, limits, and extensions of analytic varieties, Lecture Notes in Mathematics, No. 19, Springer-Verlag, Berlin-New York, 1966. · Zbl 0142.33801
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.