Euler characteristic of the Milnor fibre

of plane singularities

Author:
A. Melle-Hernández

Journal:
Proc. Amer. Math. Soc. **127** (1999), 2653-2655

MSC (1991):
Primary 32S05, 14H20; Secondary 14B05

Published electronically:
May 19, 1999

MathSciNet review:
1676312

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Abstract | References | Similar Articles | Additional Information

Abstract: We give a formula for the Euler characteristic of the Milnor fibre of any analytic function 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 The goal of the formula is that it use neither the resolution nor the deformations of Moreover, it can be use for giving an algorithm to compute it.

**[A]**Norbert A’Campo,*La fonction zêta d’une monodromie*, Comment. Math. Helv.**50**(1975), 233–248 (French). MR**0371889****[BWK]**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****[BK]**Egbert Brieskorn and Horst Knörrer,*Plane algebraic curves*, Birkhäuser Verlag, Basel, 1986. Translated from the German by John Stillwell. MR**886476****[EN]**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****[GPS]**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.**[M]**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****[S]**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**, 10.1007/BFb0086388

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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

DOI:
https://doi.org/10.1090/S0002-9939-99-05423-4

Keywords:
Euler characteristic,
Milnor fibration,
Milnor fibre

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

Article copyright:
© Copyright 1999
American Mathematical Society