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Abstrakty
We give an effective formula for the improper isolated multiplicity of a polynomial mapping. Using this formula we construct, for a given deformation of a holomorphic mapping with an isolated zero at zero, a stratification of the space of parameters such that the Łojasiewicz exponent is constant on each stratum.
Słowa kluczowe
Wydawca
Rocznik
Tom
Strony
55--62
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
autor
- Faculty of Mathematics and Computer Science, University of Łódź, S. Banacha 22, 90-238 Łódź, Poland
autor
- Faculty of Mathematics and Computer Science, University of Łódź, S. Banacha 22, 90-238 Łódź, Poland
autor
- Faculty of Mathematics and Computer Science, University of Łódź, S. Banacha 22, 90-238 Łódź, Poland
Bibliografia
- [1] R. Achilles, P. Tworzewski, and T. Winiarski, On improper isolated intersection in complex analytic geometry, Ann. Polon. Math. 51 (1990), 21–36.
- [2] R. N. Draper, Intersection theory in analytic geometry, Math. Ann. 180 (1969), 175–204.
- [3] M. Lejeune-Jalabert and B. Teissier, Séminaire Lejeune-Teissier: Clôture intégrale des idéaux et équisingularité : Chapitre 1, Université Scientifique et Médicale de Grenoble, Laboratoire de mathématiques pures associé au C.N.R.S., 1974.
- [4] S. Łojasiewicz, Introduction to Complex Analytic Geometry, Birkhäuser, 1991.
- [5] H. Matsumura, Commutative Ring Theory, Cambridge Stud. Adv. Math. 8, Cambridge Univ. Press, Cambridge, 1989.
- [6] A. Płoski, Multiplicity and the Łojasiewicz exponent, in: Singularities (Warszawa, 1985), Banach Center Publ. 20, PWN, Warszawa, 1988, 353–364.
- [7] A. Płoski, Semicontinuity of the Łojasiewicz exponent, Univ. Iagel. Acta Math. 48 (2010), 103–110.
- [8] T. Rodak, Reduction of a family of ideals, Kodai Math. J. 38 (2015), 201–208.
- [9] T. Rodak and S. Spodzieja, Effective formulas for the local Łojasiewicz exponent, Math. Z. 268 (2011), 37–44.
- [10] A. Różycki, Effective calculations of the multiplicity of polynomial mappings, Bull. Sci. Math. 138 (2014), 343–355.
- [11] S. Spodzieja, Multiplicity and the Łojasiewicz exponent, Ann. Polon. Math. 73 (2000), 257–267.
- [12] J. Stückrad and W. Vogel, An algebraic approach to the intersection theory, in: The Curves Seminar at Queens, Vol. II (Kingston, Ont., 1981/1982), Queen’s Papers in Pure Appl. Math. 61, exp. no. A, Queen’s Univ., Kingston, ON, 1982, 32 pp.
- [13] B. Teissier, Variétés polaires. I. Invariants polaires des singularités d’hypersurfaces, Invent. Math. 40 (1977), 267–292.
- [14] B. Teissier, Polyèdre de Newton jacobien et équisingularité, in: Seminar on Singularities (Paris, 1976/1977), Publ. Math. Univ. Paris VII 7, Univ. Paris VII, Paris, 1980, 193–221.
- [15] P. Tworzewski, Intersection theory in complex analytic geometry, Ann. Polon. Math. 62 (1995), 177–191.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-cab24407-7b03-44ee-bf24-b12fca160315