On the Łojasiewicz exponent near the fibre of a polynomial

• Autorzy: Skalski G.
• Języki publikacji: EN

Abstrakty

EN

The equivalence of the definitions of the Łojasiewicz exponent introduced by Ha and by Chądzyński and Krasiński is proved. Moreover we show that if the above exponents are less than -1 then they are attained at a curve meromorphic at infinity.

Słowa kluczowe

EN

polynomial; Łojasiewicz exponent

PL

wielomian; eksponenta Łojasiewicza

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2004
• Tom: Vol. 52, nr 3
• Strony: 231--236
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Skalski G.

• Faculty of Mathematics, University of Łódź, S. Banacha 22, 90-238 Łódź, Poland,

Bibliografia

• [1] R. Benedetti and J. J. Risler, Real Algebraic and Semi-Algebraic Sets, Hermann, Paris, 1990.
• [2] J. Chądzyński and T. Krasiński, The gradient of a polynomial at infinity, Kodai Math. J. 26 (2003), 317-339.
• [3] -, -, A set on which the Łojasiewicz exponent at infinity is attained, Ann. Polon. Math. 67 (1997), 191-197.
• [4] J. Gwoździewicz and S. Spodzieja, Łojasiewicz gradient inequality in a neighbourhood of the fibre, Faculty of Math., Univ. of Łódź, preprint (http://www.math.uni.lodz.pl/preprints) (2002).
• [5] H. V. Ha, Nombres de Łojasiewicz et singularités à l'infini des polynômes de deux variables complexes, C. R. Acad. Sci. Paris 311 (1990), 429-432.
• [6] J. Milnor, On Singular Points of Complex Hypersurfaces, Ann. of Math. Stud. 61, Princeton Univ. Press, 1968; Russian translation, Moscow, 1971.
• [7] A. Nemethi and A. Zaharia, Milnor fibration at infinity, Indag. Math. 3 (1992), 323-335.