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On the topology of full non-degenerate complete intersection variety

Published online by Cambridge University Press:  22 January 2016

Mutsuo Oka
Mutsuo Oka*
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo 152, Japan
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Let h1(u),…, hk(u) be Laurent polynomials of m-variables and let

be a non-degenerate complete intersection variety. Such an intersection variety appears as an exceptional divisor of a resolution of non-degenerate complete intersection varieties with an isolated singularity at the origin (Ok4]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 121 , March 1991 , pp. 137 - 148
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

References

[A-F] Andreotti, A. and Frankel, T., The Lefschetz theorem on hyperplane sections, Ann. of Math., 69 (1959), 713–717.Google Scholar
[B1] Broughton, S. A., On the topology of polynominal hypersurfaces, Proc. Sympos. Pure Math., 40, Part 1 (1983), 167–178.Google Scholar
[B2] Broughton, S. A., Milnor numbers and the topology of polynomial hypersurfaces, Invent. Math., 92 (1988), 217–241.Google Scholar
[Da] Danilov, V. I., The geometry of toric varieties, Russian Math. Surveys, 33:2 (1978), 97–154.CrossRefGoogle Scholar
[Da-Kh] Danilov, V. I. and Khovanskii, A. G., Newton Polyhedra and an algorithm for computing Hodge-Deligne numbers, Math. USSR Izv., 29, No. 2 (1987), 279–298.Google Scholar
[De] Demazure, M., Sous-groupes algébriques de rang maximum du groupe de Cremona, Ann. Sci. École Norm. Sup., (4) 3 (1970), 507–588.Google Scholar
[E] Ehlers, F., Eine Klasse komplexer Mannigfaltigkeiten und die Auflösung einer isolierter Singularitäten, Math. Ann., 218 (1975), 127–156.Google Scholar
[Grl-Hm] Greuel, G. M. and Hamm, H. A., Invarianten quasihomogener vollstandiger Durchschnitte, Invent. Math., 49 (1978), 67–86.Google Scholar
[Grf-Hr] Griffiths, P. and Harris, J., “Principles of Algebraic Geometry,” A Wiley-Interscience Publication, New York-Chichester-Brisbane-Tronto, 1978.Google Scholar
[H2] Hamm, H. A., Genus Xy of quasihomogene complete intersections, Funkts. Anal. Prilozhen., 11, No. 1 (1977), 87–88.Google Scholar
[K-K-M-S] Kempf, G., Knudsen, F., Mumford, D. and Saint-Donat, B., “Toroidal Embeddings, Lecture Notes in Math.” Springer, Berlin-Heidelberg-New York, 1973.Google Scholar
[Kh1] Khovanskii, A. G., Newton polyhedra and toral varieties, Funkts. Anal. Prilozhen., 11, No. 4 (1977), 56–67.Google Scholar
[Kh2] Khovanskii, A. G., Newton polyhedra and the genus of complete intersections, Funkts. Anal. Prilozhen., 12, No. 1 (1977), 51–61.Google Scholar
[K] Kouchnirenko, A. G., Polyèdres de Newton et Nombres de Milnor, Invent. Math., 32 (1976), 1–32.Google Scholar
[Lo] Looijenga, E. J. N., “Isolated Singular Points on Complete Intersections,” London Mathematical Society Lecture Note Series, Cambridge University Press, London-New York, 1983.Google Scholar
[M] Milnor, J., Singular points of complex hypersurface, Annals Math. Studies 61 (1968), Princeton Univ. Press, Princeton.Google Scholar
[Od1] Oda, T., “Lectures on Torus Embeddings and Applications,” Tata Inst. Fund. Research, Springer-Verlag, Berlin-Heiderberg-New York, 1978.Google Scholar
[Od2] Oda, T., “Convex Bodies and Algebraic Geometry,” Springer, Berlin-Heidelberg-New York, 1987.Google Scholar
[Ok1] Oka, M., On the bifurcation of the multiplicity and topology of the Newton boundary, J. Math. Soc. Japan, 31 (1979), 435–450.Google Scholar
[Ok2] Oka, M., On the topology of the Newton boundary II, J. Math. Soc. Japan, 32 (1980), 65–92.Google Scholar
[Ok3] Oka, M., On the resolution of hypersurface singularities, Advanced Studies in Pure Mathematics, 8 (1986), 405–436.Google Scholar
[Ok4] Oka, M., Principal zeta-function of non-degenerate complete intersection singularity, J. Fac Sci., Univ. Tokyo, 37, No. 1 (1990), 11–32.Google Scholar
[Ok5] Oka, M., Examples of algebraic surfaces, in “A Fete of Topology,” Academic Press, Boston-San Diego-New York, 1988, pp. 355–363.Google Scholar
[S] Spanier, E. H., “Algebraic Topology,” Springer, New York-Heidelberg-Berlin, 1966.Google Scholar
[V] Verdier, J. P., Stratifications de Whitney et théorème de Bertini-Sard, Invent. Math., 36 (1976), 295–312.Google Scholar
[W] Wolf, J., Differentiable fibre spaces and mappings compatible with Riemannian metrics, Michigan Math. J., 11 (1964), 65–70.Google Scholar