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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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 $f$ 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.


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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: http://dx.doi.org/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
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