Singularities pp 317-343 | Cite as

Sur la topologie des polynômes complexes

  • Enrique Artal-Bartolo
  • Pierrette Cassou-Noguès
  • Alexandru Dimca
Chapter
Part of the Progress in Mathematics book series (PM, volume 162)

Résumé

Soit f ∊ ℂ[x i,... ,x n ] un polynôme de degré d. On sait [P], [ST] qu’il existe un ensemble fini A C C tel que
$$f:{C^n}\backslash {f^{ - 1}}(\Lambda ) \to C\backslash \Lambda $$
est une fibration localement triviale. Dorénavant A désigne le plus petit ensemble qui possède cette propriété. Si t ∊ Λ, la fibre F t = f −1(t) est appellée fibre irrégulière de f, sinon elle est dite régulière ou générique. Soit δ un nombre réel positif assez petit, δ ∉ Λ. On note
$${D_\delta } = \{ t \in C|\left| t \right| < \delta \} ,{S_\delta } = \partial {{\bar D}_\delta }et{T_\delta } = {f^{ - 1}}({D_\delta })$$
Si la fibre F 0 est régulière, alors on a les deux faits suivants.
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Copyright information

© Springer Basel AG 1998

Authors and Affiliations

  • Enrique Artal-Bartolo
    • 1
  • Pierrette Cassou-Noguès
    • 2
  • Alexandru Dimca
    • 2
  1. 1.Departamento de MatemáticasUniversidad de ZaragozaZaragozaEspagne
  2. 2.Laboratoire de mathématiques puresUniversité Bordeaux ITalenceFrance

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