On the topology of a generic fibre of a polynomial function
作者:
E. Artal,
I. Luengo,
A. Melle,
期刊:
Communications in Algebra
(Taylor Available online 2000)
卷期:
Volume 28,
issue 4
页码: 1767-1787
ISSN:0092-7872
年代: 2000
DOI:10.1080/00927870008826926
出版商: Gordon and Breach Science Publishers Ltd.
关键词: Complex polynomial function;atypical values at infinity;14F45;14D25;32S15;32S60
数据来源: Taylor
摘要:
In this work we study the topologies of the fibres of some families of complex polynomial functions with isolated critical points. We consider polynomials with some transversality conditions at infinity and compute explicitly its global Milnor number μ(f). the invariant λ(f) and therefore the Euler characteristic of its generic fibre. We show that under some mild ransversality condition (transversal at infinity) the behavior offat infinity is good and the topology of the generic fibre is determined by the two homogeneous parts of higher degree offFinally we study families of polynomials, called two-term polynomials. This polynomials may have atypical values at infinity. Given such a two-term polynomialfwe characterize its atypical values by some invariants off. These polynomials are a source of interesting examples.
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