On the topology of the Newton boundary II generic weighted homogeneous singularity

Mutsuo OKA

doi:10.2969/jmsj/03210065

On the topology of the Newton boundary II

generic weighted homogeneous singularity

Mutsuo OKA

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1980 年 32 巻 1 号 p. 65-92

DOI https://doi.org/10.2969/jmsj/03210065

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Published: 1980 Received: 1978/04/10 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) N. A'Campo, La fonction zeta d'une monodromie, Comm. Math. Helv., 50 (1975), 233-248.
2) E. Brieskorn, Beispiele zur Differentialtopologie von Singularitäten, Invent. Math., 2 (1961), 1-14.
3) A. Durfee, Diffeomorphism classification of isolated hypersurface singularities, Thesis, Cornell Univ., 1971.
4) C. Ehresmann, Sur l'espaces fibrés differentiables, C.R. Acad. Sci., Paris, 224 (1974), 1611-1612.
5) H. Hamm and Lê Dung Tráng, Un Théorème de Zariski du type du Lefschetz, Ann. Sci. L'Ecole Norm. Sup., 6 (1973), 317-366.
6) M. Kato and Y. Matsumoto, On the connectivity of the Milnor fiber of a holomorphic function at a critical point, Proc. Int. Conf. on Manifolds, Tokyo 1973, 131-136.
7) A.G. Kouchnirenko, Polyèdres de Newton et nombres de Milnor, Invent. Math., 32 (1976), 1-31.
8) Lê Dung Tráng, La monodromie n'a pas de points fixes, J. Fac. Sci. Univ. Tokyo, 22 (1975), 409-427.
9) Lê Dung Tráng, La monodromie relative des hypersurfaces, (to appear).
10) J. Milnor, Singular points of complex hypersurfaces, Annals of Math. Studies 61, Princeton Univ. Press, 1968.
11) J. Milnor and P. Orlik, Isolated singularities defined by weighted homogeneous polynomials, Topology, 9 (1970), 285-293.
12) D. Mumford, Topology of normal singularities of an algebraic surfaces and a criterion for simplicity, Publ. Math. I.H.E.S., 9 (1961).
13) M. Oka, On the cohomology structures of projective varieties, Manifolds-Tokyo 1973, 137-143, Univ. of Tokyo Press, 1975.
14) M. Oka, The monodromy of a curve with ordinary double points, Invent. Math., 27 (1974), 157-164.
15) M. Oka, On the topology of the complement of a hypersurface in Pⁿ, Quart. J. Math. Oxford (2), 28 (1977), 229-242.
16) M. Oka, On the bifurcation of the multiplicity and topology of the Newton boundary, J. Math. Soc. Japan, 31 (1979), 435-450.
17) P. Orlik and P.Wagreich, Isolated singularities of algebraic surfaces with C^*-action, Ann. of Math., 93 (1971), 205-228.
18) F. Pham, Formules de Picard-Lefschetz généralizées et ramification des intégrales, Bull. Soc. Math. France, 93 (1965), 333-367.
19) E. Spanier, Algebraic topology, 1965, McGraw-Hill.
20) A.N. Varchenko, Zeta function of monodromy and Newton's diagram, Invent. Math., 37 (1976), 253-262.

Right : [1] N. A'Campo, La fonction zeta d'une monodromie, Comm. Math. Helv., 50 (1975), 233-248.
[2] E. Brieskorn, Beispiele zur Differentialtopologie von Singularitäten, Invent. Math., 2 (1961), 1-14.
[3] A. Durfee, Diffeomorphism classification of isolated hypersurface singularities, Thesis, Cornell Univ., 1971.
[4] C. Ehresmann, Sur l'espaces fibrés differentiables, C. R. Acad. Sci., Paris, 224 (1974), 1611-1612.
[5] H. Hamm and Lê Dung Tráng, Un Théorème de Zariski du type du Lefschetz, Ann. Sci. L'Ecole Norm. Sup., 6 (1973), 317-366.
[6] M. Kato and Y. Matsumoto, On the connectivity of the Milnor fiber of a holomorphic function at a critical point, Proc. Int. Conf. on Manifolds, Tokyo 1973, 131-136.
[7] A. G. Kouchnirenko, Polyèdres de Newton et nombres de Milnor, Invent. Math., 32 (1976), 1-31.
[8] Lê Dung Tráng, La monodromie n'a pas de points fixes, J. Fac. Sci. Univ. Tokyo, 22 (1975), 409-427.
[9] Lê Dung Tráng, La monodromie relative des hypersurfaces, (to appear).
[10] J. Milnor, Singular points of complex hypersurfaces, Annals of Math. Studies 61, Princeton Univ. Press, 1968.
[11] J. Milnor and P. Orlik, Isolated singularities defined by weighted homogeneous polynomials, Topology, 9 (1970), 285-293.
[12] D. Mumford, Topology of normal singularities of an algebraic surfaces and a criterion for simplicity, Publ. Math. I. H. E. S., 9 (1961).
[13] M. Oka, On the cohomology structures of projective varieties, Manifolds-Tokyo 1973, 137-143, Univ. of Tokyo Press, 1975.
[14] M. Oka, The monodromy of a curve with ordinary double points, Invent. Math., 27 (1974), 157-164.
[15] M. Oka, On the topology of the complement of a hypersurface in Pⁿ, Quart. J. Math. Oxford (2), 28 (1977), 229-242.
[16] M. Oka, On the bifurcation of the multiplicity and topology of the Newton boundary, J. Math. Soc. Japan, 31 (1979), 435-450.
[17] P. Orlik and P.Wagreich, Isolated singularities of algebraic surfaces with C^*-action, Ann. of Math., 93 (1971), 205-228.
[18] F. Pham, Formules de Picard-Lefschetz généralizées et ramification des intégrales, Bull. Soc. Math. France, 93 (1965), 333-367.
[19] E. Spanier, Algebraic topology, 1965, McGraw-Hill.
[20] A. N. Varchenko, Zeta function of monodromy and Newton's diagram, Invent. Math., 37 (1976), 253-262.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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