## Hokkaido Mathematical Journal

### On the {\L}ojasiewicz exponent

Zbigniew JELONEK

#### 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.

#### Article information

Source
Hokkaido Math. J., Volume 35, Number 2 (2006), 471-485.

Dates
First available in Project Euclid: 29 September 2010

https://projecteuclid.org/euclid.hokmj/1285766366

Digital Object Identifier
doi:10.14492/hokmj/1285766366

Mathematical Reviews number (MathSciNet)
MR2254661

Zentralblatt MATH identifier
1108.14050

#### Citation

JELONEK, Zbigniew. On the {\L}ojasiewicz exponent. Hokkaido Math. J. 35 (2006), no. 2, 471--485. doi:10.14492/hokmj/1285766366. https://projecteuclid.org/euclid.hokmj/1285766366