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

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

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]**N. A'Campo,*La fonction zeta d'une monodromie*, Comm. Math. Helvetici**50**(1975), 233-248. MR**51:8106****[BWK]**T. Becker, V. Weispfenning and H. Kredel,*Gröbner Bases: A Computational Approach to Commutative Algebra, Graduate Text in Math., vol. 141*, Springer-Verlag, Berlin-Heidelberg-New York, 1991. MR**95e:13018****[BK]**E. Brieskorn and H. Knörrer,*Plane algebraic curves*, Birkhäuser, Basel-Boston-Stuttgart, 1986. MR**88a:14001****[EN]**D. Eisenbud and W. Neumann,*Three-dimensional link theory and invariants of plane curve singularities*, Ann. of Math. Studies, No. 110, Princeton Univ. Press, Princeton, N.J., 1985. MR**87g:57007****[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]**J. Milnor,*Singular points of complex hypersurfaces, Ann. of Math. Studies, No. 61*, Princeton Univ. Press, Princeton, N.J., 1968. MR**39:969****[S]**R. Schrauwen,*Deformations and the Milnor number of non isolated plane curve singularities*, Singularity theory and its applications. Part I, proceedings Warwick 1989. Lecture Notes in Math., vol. 1462, Springer-Verlag, Berlin-Heidelberg-New York, 1991, pp. 276-291. MR**92j:32128**

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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