Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Euler characteristic of the Milnor fibre of plane singularities
HTML articles powered by AMS MathViewer

by A. Melle-Hernández PDF
Proc. Amer. Math. Soc. 127 (1999), 2653-2655 Request permission

Abstract:

We give a formula for the Euler characteristic of the Milnor fibre of any analytic function $f$ of two variables. This formula depends on the intersection multiplicities, the Milnor numbers and the powers of the branches of the germ of the curve defined by $f.$ The goal of the formula is that it use neither the resolution nor the deformations of $f.$ Moreover, it can be use for giving an algorithm to compute it.
References
  • Norbert A’Campo, La fonction zêta d’une monodromie, Comment. Math. Helv. 50 (1975), 233–248 (French). MR 371889, DOI 10.1007/BF02565748
  • Thomas Becker and Volker Weispfenning, Gröbner bases, Graduate Texts in Mathematics, vol. 141, Springer-Verlag, New York, 1993. A computational approach to commutative algebra; In cooperation with Heinz Kredel. MR 1213453, DOI 10.1007/978-1-4612-0913-3
  • Egbert Brieskorn and Horst Knörrer, Plane algebraic curves, Birkhäuser Verlag, Basel, 1986. Translated from the German by John Stillwell. MR 886476, DOI 10.1007/978-3-0348-5097-1
  • David Eisenbud and Walter Neumann, Three-dimensional link theory and invariants of plane curve singularities, Annals of Mathematics Studies, vol. 110, Princeton University Press, Princeton, NJ, 1985. MR 817982
  • G.M. Greuel, G. Pfister, H. Schoenemann, SINGULAR. A computer algebra system for singularity theory and algebraic geometry, It is available via anonymous ftp from helios.mathematik.uni-kl.de.
  • John Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies, No. 61, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. MR 0239612
  • Rob Schrauwen, Deformations and the Milnor number of nonisolated plane curve singularities, Singularity theory and its applications, Part I (Coventry, 1988/1989) Lecture Notes in Math., vol. 1462, Springer, Berlin, 1991, pp. 276–291. MR 1129038, DOI 10.1007/BFb0086388
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 32S05, 14H20, 14B05
  • Retrieve articles in all journals with MSC (1991): 32S05, 14H20, 14B05
Additional Information
  • A. Melle-Hernández
  • Affiliation: Departamento de Algebra, Facultad de CC. Matemáticas, Universidad Complutense de Madrid, Madrid 28040, Spain
  • Email: amelle@eucmos.sim.ucm.es
  • Received by editor(s): July 24, 1996
  • Received by editor(s) in revised form: June 27, 1997
  • Published electronically: May 19, 1999
  • Additional Notes: This work was done under the partial support of CAYCIT PB94-291.
  • Communicated by: Ron Donagi
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 2653-2655
  • MSC (1991): Primary 32S05, 14H20; Secondary 14B05
  • DOI: https://doi.org/10.1090/S0002-9939-99-05423-4
  • MathSciNet review: 1676312