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4 Bulletin of the Polish Academy of Sciences. Mathematics

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Multiplicity and Semicontinuity of the Łojasiewicz Exponent

Rodak T., Różycki A., Spodzieja S.

Bulletin of the Polish Academy of Sciences. Mathematics

2016

Vol. 64, no. 1

55--62

We give an effective formula for the improper isolated multiplicity of a polynomial mapping. Using this formula we construct, for a given deformation of a holomorphic mapping with an isolated zero at zero, a stratification of the space of parameters such that the Łojasiewicz exponent is constant on each stratum.

The Fedoryuk condition and the Łojasiewicz exponent near a fibre of a polynomial

Rodak T.

Bulletin of the Polish Academy of Sciences. Mathematics

2004

Vol. 52, nr 3

227-229

We give a description of the set of points for which the Fedoryuk condition fails in terms of the Łojasiewicz exponent at infinity near a fibre of a polynomial.

The Łojasiewicz exponent of the gradient at infinity

Rodak T.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 1

93-98

Let f [a member of a set] C[x, y] and deg f = deg[sub y] f [is more than or equal to] 2. In this paper we prove that the Łojasiewicz exponent L[infinity] (grad f) of the gradient of f at infinity is attained on the curve f'y=0.

On some characterization of proper polynomial mappings

Rodak T., Spodzieja S.

Bulletin of the Polish Academy of Sciences. Mathematics

2000

Vol. 48, no 2

157-164

It is well known that a proper, in the classical topology, polynomial mapping is closed in the Zariski topology. In the paper we prove that the inverse is true. Namely, any non-constant polynomial mapping from [C^n] into [C^m] which is closed in the Zariski topology is proper in the classical topology.