A set on which the local Lojasiewicz exponent is attained
Abstract
Let U be a neighbourhood of 0 ∈ Cn.We show that for a holomorphic mapping F = (f1,...,fm) : U -> Cm, F(0) = 0, the Lojasiewicz exponent of F at 0 is attained on the set z ∈ U : f1(z)...fm(z) = 0.
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