POLES OF THE CURRENT |f|2λ OVER AN ISOLATED SINGULARITY

BARLET, D.; MAIRE, H.-M.

doi:10.1142/s0129167x00000313

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Journal article

POLES OF THE CURRENT |f|2λ OVER AN ISOLATED SINGULARITY

BARLET, D. Université H. Poincaré et Institut, Universitaire de France, Institut E. Cartan UMR 7502 UHP/CNRS/INRIA, Boîte postale 239, F-54506 Vandoeuvre-les-Nancy, France
MAIRE, H.-M. Section de Mathématiques, Université de Genève, Case postale 240, CH-1211 Genève 24, Switzerland

2012-1-25

Published in:

International Journal of Mathematics. - World Scientific Pub Co Pte Lt. - 2000, vol. 11, no. 05, p. 609-635

General Mathematics

English Let (X, 0) be the germ of a normal space of dimension n+1 with an isolated singularity at 0 and let f be a germ of holomorphic function with an isolated regularity at 0. We prove that the meromorphic extension of the current [Formula: see text] has a pole of order k at λ=-m-r for m∈ℕ large enough and r∈[0, 1[ if , and only if, e-2iπr is an eigenvalue with nilpotency order k of the monodromy of f acting on Hn(F)/J, where F is the Milnor fibre of f and J is the image of the restriction map Hn(X\{0})→Hn(F).

Language

English

Open access status

closed

Identifiers

DOI 10.1142/s0129167x00000313
ISSN 0129-167X

Persistent URL

https://sonar.ch/global/documents/46024

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