Abstract. An effective formula for the Lojasiewicz exponent of a polynomial mapping of C 2 into C 2 at an isolated zero in terms of the resultant of its components is given.
Pełen tekst
(3.3) R e m a r k. The following example shows that assumption (iv) can- not be weakened. Let H(z) = (f (x, y), g(x, y)) = ((y 3 − x) 2 , y 2 x). One can easily find, by using the main theorem of [CK 1 ], that L 0 (H) = 6, whereas Q(w, x) = x 10 −2ux 8 +u 2 x 6 −2v 3 x 5 −2uv 3 x 3 +v 6 and min µ−1 i=0 ord Q µ−ii
A|z| L0
|x| ∼ |z|, |z| L0
(8) A 1 |z| L0
A|x| L0
Powiązane dokumenty
Therefore from the abc-conjecture and Lemma 3 it follows that there are only a finite number of admissible reduced pairs (A, C) satisfying α(A, C) < 1/2−ε.. The number of
Since all the known nonlinear mappings preserving normality (or the Cauchy distribution) have discontinuities it is natural to conjecture that under continuity assumption the
Hence and from Proposition 3 it follows that the problem of finding the Lojasiewicz exponent for X, Y reduces to the case when X and Y generate irreducible germs at 0.. Let now Z be
We prove that the exponent is a rational number, that it is attained on a meromorphic curve (Prop. 1), and we give a condition equivalent to the properness of regular mappings (Cor..
Key words and phrases: Dugundji extension property, linear extender, π-embedding, retract, measurable cardinal, generalized ordered space, perfectly normal, product.. Research of
Moreover, the problem of determining whether every holomorphic function on an open set in C n can be approxi- mated by polynomials in the open-closed topology is linked to the
The main result of the present paper is Theorem 3, which is a generalization of the C 0 -closing lemma to the case of a not necessarily compact manifold.. Moreover, under
1. Let M be an m-dimensional normed complex vector space.. By the above lemma our condition can be carried over—in a classical manner—to the case of manifolds. It suffices to show