A set on which the local Lojasiewicz exponent is attained

1998/02/16 by J. Chadzynski, T. Krasinski
Mathematics · #math.CV #msc:32S05

paper · pdf

published as Ann. Polon. Math. 67 (1997) 297-301 · 4 pages, AMSTeX 2.1

arxiv created 1998/02/16 · arxiv updated 2009/11/30

Abstract

Let U be a neighbourhood of 0 ∈ Cⁿ.We show that for a holomorphic mapping F = (f₁,...,f_m) : U -> C^m, F(0) = 0, the Lojasiewicz exponent of F at 0 is attained on the set z ∈ U : f₁(z)...f_m(z) = 0.

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