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Dualität in der lokalen Kohomologie isolierter Singularitäten. (German) Zbl 0417.14003

MSC:
14B05 Singularities in algebraic geometry
14B15 Local cohomology and algebraic geometry
14B07 Deformations of singularities
32C37 Duality theorems for analytic spaces
32S05 Local complex singularities
14M10 Complete intersections
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References:
[1] Andreotti, A., Grauert, H.: Théorèmes de finitude pour la cohomologie des espaces complexes. Bull. Soc. math. France90, 193–159 (1962) · Zbl 0106.05501
[2] Bănică, C., Stănăsilă, O.: Méthodes algébriques dans la théorie globale des espaces complexes. Paris: Gauthiers-Villars 1977
[3] Bloom, T., Herrera, M.: De Rham cohomology of analytic space. Invent. Math.7, 275–296 (1969) · Zbl 0175.37301
[4] Brieskorn, E.: Die Hierarchie der 1-modularen Singularitäten. Manuscripta Math.27, 183–219 (1979) · Zbl 0406.58009
[5] Buchsbaum, D., Rim, D.S.: A generalized Koszul complex. II. Depth and multiplicity. Am. Math. Soc.111, 197–224 (1964) · Zbl 0131.27802
[6] Giusti, M.: Sur les singularités isolées d’intersections complètes quasi-homogènes. Ann. Inst. Fourier27, 163–192 (1977) · Zbl 0353.14003
[7] Greuel, G.-M.: Der Gauß-Manin-Zusammenhang isolierter Singularitäten von vollständigen Durchschnitten. Math. Ann.214, 235–266 (1975) · Zbl 0285.14002
[8] Greuel, G.-M.: Deformationen spezieller Kurvensingularitäten und eine Formel von Deligne (preprint)
[9] Greuel, G.-M., Hamm, H.: Invarianten quasihomogener vollständiger Durchschnitte. Invent. Math.49, 67–86 (1978) · Zbl 0394.32006
[10] Grothendieck, A.: Local cohomology. In: Lecture Notes in Mathematics, Vol.41. Berlin, Heidelberg, New York: Springer 1967 · Zbl 0185.49202
[11] Grothendieck, A., Dieudonné, J.: Éléments de géométrie algébrique. IHES Publ. Math.11, 5–167 (1962)
[12] Hamm, H.: Lokale topologische Eigenschaften komplexer Räume. Math. Ann.191, 235–252 (1971) · Zbl 0214.22801
[13] Herzog, J., Kunz, E.: Der kanonische Modul eines Cohen-Macaulay Rings. In: Lecture Notes in Mathematics, Vol. 238. Berlin, Heidelberg, New York: Springer 1971 · Zbl 0231.13009
[14] Kunz, E.: Residuen von Differentialformen auf Cohen-Macaulay Varietäten. Math. Z.152, 165–189 (1977) · Zbl 0342.14022
[15] Laufer, H.: On Serre duality and envelopes of holomorphy. Trans. Am. Math. Soc.128, 414–436 (1967) · Zbl 0166.33903
[16] Lê Dũng Tráng: Calculation of milnor number of isolated singularity of complete intersection. Funkcional. Anal. i Prilozen.8, 45–49 (1974) · Zbl 0351.32007
[17] Lipman, J.: Vortrag in Oberwolfach, Mai 1979
[18] Milnor, J.: Singular points of complex hypersurfaces. In: Annals of Mathematical Studies, Vol. 61. Princeton: Princeton University Press 1968 · Zbl 0184.48405
[19] Naruki, I.: Some remarks on isolated singularity and their application to algebraic manifolds. Publ. Res. Inst. Math. Sci.13, 17–46 (1977) · Zbl 0384.14002
[20] Saito, K.: Quasihomogene isolierte Singularitäten von Hyperflächen. Invent. Math.14, 123–142 (1971) · Zbl 0224.32011
[21] Serre, J.P.: Un théorème de dualité. Comment. Math. Helv.29, 9–26 (1955) · Zbl 0067.16101
[22] Siu, Y.-T.: Analytic sheaf cohomology groups of dimensionn ofn-dimensional complex spaces. Trans. Am. Math. Soc.143, 77–94 (1969) · Zbl 0186.40404
[23] Siu, Y.-T., Trautmann, G.: Gap-sheaves and extension of coherent analytic subsheaves. In: Lecture Notes in Mathematics, Vol. 172. Berlin, Heidelberg, New York: Springer 1971 · Zbl 0208.10403
[24] Steenbrink, J.: Intersection form for quasi-homogeneous singularities. Compositio Math.34, 211–223 (1977) · Zbl 0347.14001
[25] Steenbrink, J.: Mixed hodge structure on the vanishing cohomology. In: Real and complex singularities, Oslo 1976. Proceedings of the Nordic Summer School NAVF, Symposium in Mathematics · Zbl 0303.14002
[26] Teissier, B.: Deformations à type topologique constant. In: Sém. Doudy-Verdier 1971–1972. Asterisque16 (1974)
[27] Tjurina, G.N.: Locally semiuniversal flat deformations of isolated singularities of complex spaces. Math. USSR-Izv.3, 967–999 (1969) · Zbl 0209.11301
[28] Varchenko, A.N.: Contact structures and isolated singularities. Bericht für den Sonderforschungs-bereich ”Theoretische Mathematik” in Bonn, März 1977
[29] Wahl, J.: Smoothings of normal surface singularities (preprint) · Zbl 0484.14012
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