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dc.contributor.authorBrzostowski, Szymon
dc.contributor.editorKrasiński, Tadeusz
dc.contributor.editorSpodzieja, Stanisław
dc.identifier.citationBrzostowski S., A note on the Łojasiewicz exponent of non-degenerate isolated hypersurface singularities, in: Analytic and Algebraic Geometry 3, T. Krasiński, S. Spodzieja (red.), WUŁ, Łódź 2019, doi: 10.18778/8142-814-9.04.pl_PL
dc.description.abstractWe prove that in order to find the value of the Łojasiewicz exponent ł(f) of a Kouchnirenko non-degenerate holomorphic function f : (Cn; 0) → (C; 0) with an isolated singular point at the origin, it is enough to find this value for any other (possibly simpler) function g : (Cn; 0) → (C; 0), provided this function is also Kouchnirenko non-degenerate and has the same Newton diagram as f does. We also state a more general problem, and then reduce it to a Teissier-like result on (c)-cosecant deformations, for formal power series with coefficients in an algebraically closed field K.pl_PL
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl_PL
dc.relation.ispartofAnalytic and Algebraic Geometry 3;
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe*
dc.titleA note on the Łojasiewicz exponent of non-degenerate isolated hypersurface singularitiespl_PL
dc.typeBook chapterpl_PL
dc.contributor.authorAffiliationUniwersytet Łódzki, Wydział Matematyki i Informatykipl_PL
dc.referencesC. Bivià-Ausina. Jacobian ideals and the Newton non-degeneracy condition. Proc. Edinb. Math. Soc. (2), 48(1):21–36, 2005.pl_PL
dc.referencesS. Brzostowski and G. Oleksik. On combinatorial criteria for non-degenerate singularities. Kodai Math. J., 39(2):455–468, 2016.pl_PL
dc.referencesS. Brzostowski and T. Rodak. The Łojasiewicz exponent via the valuative Hamburger- Noether process. In T. Krasinski and S. Spodzieja, editors, Analytic and Algebraic Geometry 2, pages 51–65. Wydawnictwo Uniwersytetu Łódzkiego, Łódz, 2017.pl_PL
dc.referencesJ. Damon and T. Gaffney. Topological triviality of deformations of functions and Newton filtrations. Invent. Math., 72(3):335–358, 1983.pl_PL
dc.referencesT. de Jong and G. Pfister. Local analytic geometry. Basic theory and applications. Advanced Lectures in Mathematics. Friedr. Vieweg & Sohn, Braunschweig, 2000.pl_PL
dc.referencesG.-M. Greuel. Constant Milnor number implies constant multiplicity for quasihomogeneous singularities. Manuscripta Math., 56(2):159–166, 1986.pl_PL
dc.referencesC. Huneke and I. Swanson. Integral closure of ideals, rings, and modules, volume 336 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 2006.pl_PL
dc.referencesA. G. Kouchnirenko. Polyèdres de Newton et nombres de Milnor. Invent. Math., 32(1):1–31, 1976.pl_PL
dc.referencesM. Lejeune-Jalabert and B. Teissier. Clôture intégrale des idéaux et équisingularité. Ann. Fac. Sci. Toulouse Math. (6), 17(4):781–859, 2008. With an appendix by Jean-Jacques Risler. An updated version of: Clôture intégrale des idéaux et équisingularité. Centre de Mathématiques, Université Scientifique et Medicale de Grenoble (1974).pl_PL
dc.referencesH. Matsumura. Commutative ring theory, volume 8 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, second edition, 1989. Translated from the Japanese by M. Reid.pl_PL
dc.referencesP. Mondal. Intersection multiplicity, Milnor number and Bernstein’s theorem. ArXiv e-prints,–41, 2016.pl_PL
dc.referencesH.-D. Nguyen, T.-S. Pha.m, and P.-D. Hoàng. Topological invariants of plane curve singularities: Polar quotients and Łojasiewicz gradient exponents. Internat. J. Math., page 1950073, Sep 2019.pl_PL
dc.referencesM. Oka. On the bifurcation of the multiplicity and topology of the Newton boundary. J. Math. Soc. Japan, 31(3):435–450, 1979.pl_PL
dc.referencesT.-S. Pha.m. On the effective computation of Łojasiewicz exponents via Newton polyhedra. Period. Math. Hungar., 54(2):201–213, 2007.pl_PL
dc.referencesA. Płoski. Multiplicity and the Łojasiewicz exponent. In Singularities (Warsaw, 1985), volume 20 of Banach Center Publ., pages 353–364. PWN, Warsaw, 1988.pl_PL
dc.referencesM. J. Saia. The integral closure of ideals and the Newton filtration. J. Algebraic Geom., 5(1):1–11, 1996.pl_PL
dc.referencesB. Teissier. Variétés polaires. I. Invariants polaires des singularités d’hypersurfaces. Invent. Math., 40(3):267–292, 1977.pl_PL
dc.referencesE. Yoshinaga. Topologically principal part of analytic functions. Trans. Amer. Math. Soc., 314(2):803–814, 1989.pl_PL
dc.referencesO. Zariski and P. Samuel. Commutative algebra. Vol. II. The University Series in Higher Mathematics. D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960.pl_PL

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