Multiplicity and Semicontinuity of the Łojasiewicz Exponent

• Autorzy: Rodak T. , Różycki A. , Spodzieja S.

Identyfikatory

DOI

10.4064/ba8041-3-2016

• Języki publikacji: EN

Abstrakty

EN

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

EN

multiplicity; effective formula; Łojasiewicz exponent

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2016
• Tom: Vol. 64, no. 1
• Strony: 55--62
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Rodak T.

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

autor

Różycki A.

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

autor

Spodzieja S.

• 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.