On C0-sufficiency of jets

Osińska-Ulrych, Beata; Skalski, Grzegorz; Spodzieja, Stanisław

dc.contributor.author	Osińska-Ulrych, Beata
dc.contributor.author	Skalski, Grzegorz
dc.contributor.author	Spodzieja, Stanisław
dc.contributor.editor	Krasiński, Tadeusz
dc.contributor.editor	Spodzieja, Stanisław
dc.date.accessioned	2017-12-13T10:26:22Z
dc.date.available	2017-12-13T10:26:22Z
dc.date.issued	2013
dc.identifier.citation	Osinska-Ulrych B., Skalski G., Spodzieja S., On C0-sufficiency of jets, [in:] Krasiński T., Spodzieja S. (eds.), Analytic and Algebraic Geometry, Łódź University Press, Łódź 2013, s. 95-113, doi: 10.18778/7969-017-6.08	pl_PL
dc.identifier.isbn	978-83-7969-017-6
dc.identifier.uri	http://hdl.handle.net/11089/23608
dc.description.abstract	The paper presents some details of the proofs by Kuiper and Kuo, and Bochnak and Łojasiewicz that refer to the impact of the Łojasiewicz exponent of gradient mappings on C0-sufficiency of jets.	pl_PL
dc.language.iso	en	pl_PL
dc.publisher	Wydawnictwo Uniwersytetu Łódzkiego	pl_PL
dc.relation.ispartof	Krasiński T., Spodzieja S. (eds.), Analytic and Algebraic Geometry, Łódź University Press, Łódź 2013;
dc.rights	Uznanie autorstwa-Użycie niekomercyjne-Bez utworów zależnych 3.0 Polska	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/pl/	*
dc.title	On C0-sufficiency of jets	pl_PL
dc.type	Book chapter	pl_PL
dc.rights.holder	© Copyright by University of Łódź, Łódź 2013	pl_PL
dc.page.number	95-113	pl_PL
dc.contributor.authorAffiliation	Faculty of Mathematics and Computer Science, University of Łódź Banacha 22, 90-238 Łódź	pl_PL
dc.references	J. Bochnak, S. Łojasiewicz, A converse of the Kuiper-Kuo theorem. Proc. of Liverpool Singularities-Symposium I (1969/70), pp.254-261, Lecture Notes in Math., vol. 192, Springer, Berlin, 1971.	pl_PL
dc.references	P. Cassou-Nogues, H. H. Vui, Théorème de Kuiper-Kuo-Bochnak-Lojasiewicz à l’infini, Ann. Fac. Sci. Toulouse Math. (6) 5 (1996), no. 3, 387–406.	pl_PL
dc.references	S. H. Chang, Y. C. Lu, On C0-sufficiency of complex jets. Canad. J. Math. 25 (1973), 874–880.	pl_PL
dc.references	J. Chądzyński, On the order of an isolated zero of a holomorphic mapping. Bull. Polish Acad. Sci. Math. 31 (1983), no. 3-4, 121–128.	pl_PL
dc.references	J. Chądzyński, T. Krasiński, The Łojasiewicz exponent of an analytic mapping of two com- plex variables at an isolated zero. Singularities (Warsaw, 1985), 139–146, Banach Center Publ., 20, PWN, Warsaw, 1988.	pl_PL
dc.references	J. Chądzyński, T. Krasński, A set on which the local Łojasiewicz exponent is attained. Ann. Polon. Math. 67 (1997), no. 3, 297–301.	pl_PL
dc.references	A. EL Khadiri, J.-Cl. Tougeron, Familles noethériennes de modules sur k [x ] et applications. (French) [Noetherian families of modules of k [x ] and applications] Bull. Sci. Math. 120 (1996), no. 3, 253–292.	pl_PL
dc.references	M. Kirschenbaum, Y. C. Lu, Sufficiency of Weierstrass jets. Canad. J. Math. 35 (1983), no. 1, 167–176.	pl_PL
dc.references	S. Koike, C0-sufficiency of jets via blowing-up. J. Math. Kyoto Univ. 28 (1988), no. 4, 605– 614.	pl_PL
dc.references	W. Kucharz, Examples in the theory of sufficiency of jets. Proc. Amer. Math. Soc. 96 (1986), no. 1, 163–166.	pl_PL
dc.references	N. H. Kuiper, C1-equivalence of functions near isolated critical points, Proc. Sym. in Infinite Dimensional Topology. (Baton Rouge, 1967), 199–218. Ann. of Math. Studies, 69, Princeton Univ. Press, Princeton, N. J., 1972.	pl_PL
dc.references	T. C. Kuo, On C0-sufficiency of jets of potential functions, Topology 8, (1969) 167–171.	pl_PL
dc.references	T. C. Kuo, Characterizations of v-sufficiency of jets. Topology 11 (1972) 115–131.	pl_PL
dc.references	T. C. Kuo, Y. C. Lu, On analytic function germs of two complex variables. Topology 16 (1977), no. 4, 299–310.	pl_PL
dc.references	T. C. Kuo, Y. C. Lu, Sufficiency of jets via stratification theory. Invent. Math. 57 (1980), no. 3, 219–226.	pl_PL
dc.references	A. Lenarcik, J. Gwoździewicz, O C0-dostateczności dżetów rzeczywistych i zespolonych, Materiały XXII Konferencji Szkoleniowej z Geometrii Analitycznej i Algebraicznej Zespolonej, Wyd. UŁ, Łódź, 2001, 7-12 (in Polish).	pl_PL
dc.references	Y. C. Lu, Sufficiency of jets in J r (2, 1) via decomposition. Invent. Math. 10 (1970), 119–127.	pl_PL
dc.references	J. Milnor, Morse Theory, Princeton Univ. Press, Princeton, N. J., 1963.	pl_PL
dc.references	M. Lejeune-Jalabert, B. Teissier, Clôture intégrale des idéaux et équisingularité, Centre de Mathématiques Ecole Polytechnique, 1974.	pl_PL
dc.references	S. Łojasiewicz, Sur le problème de la division, Studia Math. 18 (1959), 87–136; and Rozprawy Matem. 22 (1961).	pl_PL
dc.references	A. Pelczar, Remarks on sufficiency of jets. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), no. 7, 623–632.	pl_PL
dc.references	A. Pelczar, Sufficiency of jets by the method of integral inequalities, Zeszyty Nauk. Uniw. Jagielloń. Prace Mat. No. 20 (1979), 17–32.	pl_PL
dc.references	A. Płoski, Multiplicity and the Łojasiewicz exponent, in: Banach Center Publ. 20, PWN, (1988), 353–364	pl_PL
dc.references	A. Płoski, On the Jacobian ideal and sufficiency of jets. Bull. Polish Acad. Sci. Math. 41	pl_PL
dc.identifier.doi	10.18778/7969-017-6.08