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Euler characteristic of the Milnor fibre of plane singularities
Author(s):
A.
Melle-Hernández
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2653-2655.
MSC (1991):
Primary 32S05, 14H20;
Secondary 14B05
Posted:
May 19, 1999
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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.
References:
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- E. Brieskorn and H. Knörrer, Plane algebraic curves, Birkhäuser, Basel-Boston-Stuttgart, 1986. MR 88a:14001
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- 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
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- 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:
10.1090/S0002-9939-99-05423-4
PII:
S 0002-9939(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
Posted:
May 19, 1999
Additional Notes:
This work was done under the partial support of CAYCIT PB94-291.
Communicated by:
Ron Donagi
Copyright of article:
Copyright
1999,
American Mathematical Society
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