Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Łojasiewicz type inequalities and Newton diagrams

Author: Toshizumi Fukui
Journal: Proc. Amer. Math. Soc. 112 (1991), 1169-1183
MSC: Primary 58C27; Secondary 32S50
MathSciNet review: 1065945
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give an upper estimation for the Lojasiewicz exponent $ {\alpha _0}(f)$ for a nondegenerate holomorphic function germ $ f$ using the Newton polygon of $ f$.

References [Enhancements On Off] (What's this?)

  • [1] J. Bochnak and S. Lojasiewicz, A converse of the Kuiper-Kuo theorem (Proc. of Liverpool Singularities-Symposium I), Lecture Notes in Math., vol. 192, Springer-Verlag, Berlin, Heidelberg, and New York, 1971. MR 0291971 (45:1059)
  • [2] S. S. Chang and Y. C. Lu, On $ {C^0}$ sufficiency of complex jets, Canad. J. Math. 25 (1973), 874-880. MR 0343310 (49:8052)
  • [3] A. G. Kouchnirenko, Polyèdres de Newton et nombres de Milnor, Invent. Math. 32 (1976), 1-31. MR 0419433 (54:7454)
  • [4] T.-C. Kuo, On $ {C^0}$ sufficiency of jets of potential functions, Topology 8 (1969), 167-171. MR 0238338 (38:6614)
  • [5] B. Lichtin, Estimates and formulae for the $ {C^0}$-degree of sufficiency of plane curves, Proc. Sympos. Pure Math., vol. 40, 1983, pp. 155-160. MR 713244 (85c:58020)
  • [6] -, Estimation of Lojasiewicz exponents and Newton polygons, Invent. Math. 64 (1981), 417-429. MR 632982 (83b:32006)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58C27, 32S50

Retrieve articles in all journals with MSC: 58C27, 32S50

Additional Information

Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society