An effective formula for the Łojasiewicz exponent of a polynomial mapping of ℂ² into ℂ² at an isolated zero in terms of the resultant of its components is given.
@article{bwmeta1.element.bwnjournal-article-apmv61z1p95bwm, author = {J. Ch\k adzy\'nski and T. Krasi\'nski}, title = {Resultant and the \L ojasiewicz exponent}, journal = {Annales Polonici Mathematici}, volume = {62}, year = {1995}, pages = {95-100}, zbl = {0833.14003}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv61z1p95bwm} }
J. Chądzyński; T. Krasiński. Resultant and the Łojasiewicz exponent. Annales Polonici Mathematici, Tome 62 (1995) pp. 95-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv61z1p95bwm/
[000] [C] J. Chądzyński, On the order of an isolated zero of a holomorphic mapping, Bull. Polish Acad. Sci. Math. 31 (1983), 121-128. | Zbl 0554.32005
[001] [CK₁] J. Chądzyński and T. Krasiński, The Łojasiewicz exponent of an analytic mapping of two complex variables at an isolated zero, in: Singularities, S. Łojasiewicz (ed.), Banach Center Publ. 20, PWN, Warszawa, 1988, 139-146. | Zbl 0674.32004
[002] [CK₂] J. Chądzyński and T. Krasiński, On the Łojasiewicz exponent at infinity for polynomial mappings of ℂ² into ℂ² and components of polynomial automorphisms of ℂ² , Ann. Polon. Math. 57 (1992), 291-302. | Zbl 0791.14004
[003] [CP] J. Chądzyński and A. Płoski, An inequality for the intersection multiplicity of analytic curves, Bull. Polish Acad. Sci. Math. 36 (1988), 113-117. | Zbl 0699.13014
[004] [LT] M. Lejeune-Jalabert et B. Teissier, Clôture intégrale des idéaux et équisingularité, Centre de Mathématiques, École Polytechnique, 1974.
[005] [P] A. Płoski, Multiplicity and the Łojasiewicz exponent, in: Singularities, S. Łojasiewicz (ed.), Banach Center Publ. 20, PWN, Warszawa, 1988, 353-364. | Zbl 0661.32018
[006] [W] R. J. Walker, Algebraic Curves, Springer, New York, 1978.