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May 2006 On the {\L}ojasiewicz exponent
Zbigniew JELONEK
Hokkaido Math. J. 35(2): 471-485 (May 2006). DOI: 10.14492/hokmj/1285766366

Abstract

Let $\Bbb K$ be an algebraically closed field and let $X\subset \Bbb K^l$ be an $n-$dimensional affine variety of degree $D.$ We give a sharp estimation of the degree of the set of non-properness for generically-finite separable and dominant mapping $f=(f_1,...,f_n): X\to \Bbb K^n$. We show that such a mapping must be finite, provided it has a sufficiently large geometric degree. Moreover, we estimate the \L ojasiewicz exponent at infinity of a polynomial mapping $f: X\to \Bbb K^m$ with a finite number of zeroes.

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Zbigniew JELONEK. "On the {\L}ojasiewicz exponent." Hokkaido Math. J. 35 (2) 471 - 485, May 2006. https://doi.org/10.14492/hokmj/1285766366

Information

Published: May 2006
First available in Project Euclid: 29 September 2010

zbMATH: 1108.14050
MathSciNet: MR2254661
Digital Object Identifier: 10.14492/hokmj/1285766366

Subjects:
Primary: 14R99
Secondary: 14A10, 14Q20

Rights: Copyright © 2006 Hokkaido University, Department of Mathematics

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Vol.35 • No. 2 • May 2006
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