On the {\L}ojasiewicz exponent
JELONEK, Zbigniew
Hokkaido Math. J., Tome 35 (2006) no. 1, p. 471-485 / Harvested from Project Euclid
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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.
Publié le : 2006-05-15
Classification:  polynomials,  {\L}ojasiewicz exponent,  affine variety,  14R99,  14A10,  14Q20 
@article{1285766366,
     author = {JELONEK, Zbigniew},
     title = {On the {\L}ojasiewicz exponent},
     journal = {Hokkaido Math. J.},
     volume = {35},
     number = {1},
     year = {2006},
     pages = { 471-485},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1285766366}
}

JELONEK, Zbigniew. On the {\L}ojasiewicz exponent. Hokkaido Math. J., Tome 35 (2006) no. 1, pp.  471-485. http://gdmltest.u-ga.fr/item/1285766366/