A set on which the Łojasiewicz exponent at infinity is attained
Jacek Chądzyński ; Tadeusz Krasiński
Annales Polonici Mathematici, Tome 66 (1997), p. 191-197 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We show that for a polynomial mapping F=(f₁,...,fₘ):ℂn→ℂm the Łojasiewicz exponent ∞(F) of F is attained on the set z∈ℂn:f₁(z)·...·fₘ(z)=0.

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:270658 
@article{bwmeta1.element.bwnjournal-article-apmv67z2p191bwm,
     author = {Jacek Ch\k adzy\'nski and Tadeusz Krasi\'nski},
     title = {A set on which the \L ojasiewicz exponent at infinity is attained},
     journal = {Annales Polonici Mathematici},
     volume = {66},
     year = {1997},
     pages = {191-197},
     zbl = {0924.32004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv67z2p191bwm}
}

Jacek Chądzyński; Tadeusz Krasiński. A set on which the Łojasiewicz exponent at infinity is attained. Annales Polonici Mathematici, Tome 66 (1997) pp. 191-197. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv67z2p191bwm/

[000] [BR] R. Benedetti and J. J. Risler, Real Algebraic and Semi-Algebraic Sets, Hermann, Paris, 1090.

[001] [CK] J. Chądzyński and T. Krasiński, Exponent of growth of polynomial mappings of ℂ² into ℂ², in: Singularities, S. Łojasiewicz (ed.), Banach Center Publ. 20, PWN, Warszawa, 1988, 147-160.

[002] [J] Z. Jelonek, Testing sets for properness of polynomial mappings, Inst. Math., Jagiellonian University, preprint 16 (1996), 37 pp. | Zbl 0946.14039

[003] [NZ] A. Némethi and A. Zaharia, Milnor fibration at infinity, Indag. Math. 3 (1992), 323-335. | Zbl 0806.57021

[004] [P₁] A. Płoski, Newton polygons and the Łojasiewicz exponent of a holomorphic mapping of ℂ², Ann. Polon. Math. 51 (1990), 275-281. | Zbl 0764.32012

[005] [P₂] A. Płoski, A note on the Łojasiewicz exponent at infinity, Bull. Soc. Sci. Lettres Łódź 44 (17) (1994), 11-15. | Zbl 0883.32022