Notes on C0 sufficiency of quasijets

Satoshi KOIKE

doi:10.2969/jmsj/04220265

Notes on C⁰ sufficiency of quasijets

Satoshi KOIKE

著者情報

ジャーナルフリー

1990 年 42 巻 2 号 p. 265-275

DOI https://doi.org/10.2969/jmsj/04220265

詳細

Published: 1990 Received: 1988/08/15 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
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訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文受付日訂正内容: 訂正前 : 19880415
訂正後 : 19880815

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文サブタイトル訂正内容: Wrong : Dedicated to Professor Masahisa Adachi on his 60th birthday

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) V. I. Arnol'd, Normal forms of functions in the neighborhood of degenerate critical points, Uspekhi Mat. Nauk, 29 (1974), 11-49=Russian Math. Surveys, 29 (1974), 19-48.
2) J. Bochnak and J.-J. Risler, Sur les exposants de Lojasiewicz, Comment. Math. Helv., 50 (1975), 493-507.
3) M. Buchner and W. Kucharz, Topological triviality of a family of zero-sets, Proc. Amer. Math. Soc., 102 (1988), 699-705.
4) J. Damon and T. Gaffney, Topological triviality of deformations of functions and Newton filtrations, Invent. Math., 72 (1983), 335-358.
5) H. King, Topological type in families of germs, Invent. Math., 62 (1980), 1-13.
6) S. Koike, C⁰-sufficiency of jets via blowing-up, J. Math. Kyoto Univ., 28 (1988), 605-614.
7) S. Koike, A partition problem on analytic functions, Singularities and Differential Geometry, Hokkaido University Technical Report Series in Math., 7 (1988).
8) A. G. Kouchnirenko, Polyhèdres de Newton et nombres de Milnor, Invent. Math., 32 (1976), 1-31.
9) N. Kuiper, C¹-equivalence of functions near isolated critical points, Symposium on Infinite Dimensional Topology (Baton Rouge 1967), Ann. of Math. Stud., 69 (1972), 199-218.
10) T. C. Kuo, On C⁰-sufficiency of jets of potential functions, Topology, 8 (1969), 167-171.
11) T. C. Kuo, Characterizations of v-sufficiency of jets, Topology, 11 (1972), 115-131.
12) T. C. Kuo, Computation of Lojasiewicz exponent of f(x, y), Comment. Math. Helv., 49 (1974), 201-213.
13) J. Mather, Notes on topological stability, Harvard University notes, 1970.
14) J. Milnor, Singular points of complex hypersurfaces, Ann. of Math. Stud., 61, 1968.
15) M. Oka, On the bifurcation of the multiplicity and topology of the Newton boundary, J. Math. Soc. Japan, 31 (1979), 435-450.
16) M. Suzuki, The stratum with constant Milnor number of a mini-transversal family of a quasihomogeneous function of corank two, Topology, 23 (1983), 101-115.
17) J. Timourian, The invariance of Milnor's number implies topological triviality, Amer. J. Math., 99 (1977), 437-446.
18) A. N. Varcenko, A lower bound for the codimension of the stratum μ=const in terms of the mixed Hodge structure, Vestnik Moskov. Univ., 37 (1982), 28-31.
19) E. Yoshinaga, The modified analytic trivialization of real analytic families via blowing-ups, J. Math. Soc. Japan, 40 (1988), 161-179.

Right : [1] V. I. Arnol'd, Normal forms of functions in the neighborhood of degenerate critical points, Uspekhi Mat. Nauk, 29 (1974), 11-49=Russian Math. Surveys, 29 (1974), 19-48.
[2] J. Bochnak and J. -J. Risler, Sur les exposants de Lojasiewicz, Comment. Math. Helv., 50 (1975), 493-507.
[3] M. Buchner and W. Kucharz, Topological triviality of a family of zero-sets, Proc. Amer. Math. Soc., 102 (1988), 699-705.
[4] J. Damon and T. Gaffney, Topological triviality of deformations of functions and Newton filtrations, Invent. Math., 72 (1983), 335-358.
[5] H. King, Topological type in families of germs, Invent. Math., 62 (1980), 1-13.
[6] S. Koike, C⁰-sufficiency of jets via blowing-up, J. Math. Kyoto Univ., 28 (1988), 605-614.
[7] S. Koike, A partition problem on analytic functions, Singularities and Differential Geometry, Hokkaido University Technical Report Series in Math., 7 (1988).
[8] A. G. Kouchnirenko, Polyhèdres de Newton et nombres de Milnor, Invent. Math., 32 (1976), 1-31.
[9] N. Kuiper, C¹-equivalence of functions near isolated critical points, Symposium on Infinite Dimensional Topology (Baton Rouge 1967), Ann. of Math. Stud., 69 (1972), 199-218.
[10] T. C. Kuo, On C⁰-sufficiency of jets of potential functions, Topology, 8 (1969), 167-171.
[11] T. C. Kuo, Characterizations of v-sufficiency of jets, Topology, 11 (1972), 115-131.
[12] T. C. Kuo, Computation of Lojasiewicz exponent of f(x, y), Comment. Math. Helv., 49 (1974), 201-213.
[13] J. Mather, Notes on topological stability, Harvard University notes, 1970.
[14] J. Milnor, Singular points of complex hypersurfaces, Ann. of Math. Stud., 61, 1968.
[15] M. Oka, On the bifurcation of the multiplicity and topology of the Newton boundary, J. Math. Soc. Japan, 31 (1979), 435-450.
[16] M. Suzuki, The stratum with constant Milnor number of a mini-transversal family of a quasihomogeneous function of corank two, Topology, 23 (1983), 101-115.
[17] J. Timourian, The invariance of Milnor's number implies topological triviality, Amer. J. Math., 99 (1977), 437-446.
[18] A. N. Varcenko, A lower bound for the codimension of the stratum μ=const in terms of the mixed Hodge structure, Vestnik Moskov. Univ., 37 (1982), 28-31.
[19] E. Yoshinaga, The modified analytic trivialization of real analytic families via blowing-ups, J. Math. Soc. Japan, 40 (1988), 161-179.

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