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dc.contributor.authorBarroso, Evelia Rosa Garcia
dc.contributor.authorPłoski, Arkadiusz
dc.contributor.editorKrasiński, Tadeusz
dc.contributor.editorSpodzieja, Stanisław
dc.identifier.citationGarcía Barroso E. R., Płoski A., Contact exponent and the Milnor number of plane curve singularities, in: Analytic and Algebraic Geometry 3, T. Krasiński, S. Spodzieja (red.), WUŁ, Łódź 2019, doi: 10.18778/8142-814-9.08.pl_PL
dc.description.abstractWe investigate properties of the contact exponent (in the sense of Hironaka [Hi]) of plane algebroid curve singularities over algebraically closed fields of arbitrary characteristic. We prove that the contact exponent is an equisingularity invariant and give a new proof of the stability of the maximal contact. Then we prove a bound for the Milnor number and determine the equisingularity class of algebroid curves for which this bound is attained. We do not use the method of Newton's diagrams. Our tool is the logarithmic distance developed in [GB-P1].pl_PL
dc.publisherWydawnictwo Uniwersytetu Łódzkiegopl_PL
dc.relation.ispartofAnalytic and Algebraic Geometry 3;
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe*
dc.titleContact exponent and the Milnor number of plane curve singularitiespl_PL
dc.typeBook chapterpl_PL
dc.contributor.authorAffiliationDepartamento de Matematicas, Estadistica e I.O. Seccion de Matematicas, Universidad de La Laguna Apartado de Correos 456pl_PL
dc.contributor.authorAffiliationDepartment of Mathematics and Physics, Kielce University of Technologypl_PL
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dc.referencesCampillo, A. Algebroid curves in positive characteristic. Lecture Notes in Mathematics, 813. Springer Verlag, Berlin, 1980. v+168 pp.pl_PL
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dc.referencesGarcia Barroso, E., Gonzalez Perez, P. and P. Popescu-Pampu. Ultrametric spaces of branches and arborescent singularities. Singularities, Algebraic Geometry, Commutative Algebra and Related Topics. Festschrift for Antonio Campillo on the Occasion of his 65th Birthday. G.M. Greuel, L. Narvaez and S. Xambo-Descamps eds. Springer, (2018), 119-133.pl_PL
dc.referencesGarcia Barroso, E., Lenarcik, A. and A. Płoski. Newton diagrams and equivalence of plane curve germs. J. Math. Soc. Japan 59, no. 1 (2007), 81-96.pl_PL
dc.referencesGarcia Barroso, E. and A. Płoski. An approach to plane algebroid branches. Rev. Mat. Complut., 28 (1) (2015), 227-252.pl_PL
dc.referencesGarcia Barroso, E. and A. Płoski. On the Milnor Formula in arbitrary characteristic. Singularities, Algebraic Geometry, Commutative Algebra and Related Topics. Festschrift for Antonio Campillo on the occasion of his 65th Birthday. G.M. Greuel, L. Narva ez and S. Xamb o-Descamps eds. Springer, (2018), 119-133.pl_PL
dc.referencesGwoździewicz, J. and A. Płoski. On the polar quotients of an analytic plane curve. Kodai Math. Journal, Vol. 25, 1, (2002), 43-53. (1995) 199-210.pl_PL
dc.referencesHironaka, H. Introduction to the theory of in nitely near singular points, Memorias del Instituto Jorge Juan 28, Madrid 1974.pl_PL
dc.referencesMelle-Hern andez, A. and C.T. C.Wall. Pencils of curves on smooth surfaces, Proc. Lond. Math. Soc., III Ser. 83 (2), 2001, 257-278.pl_PL
dc.referencesLejeune-Jalabert, M. Sur l'equivalence des courbes algebro des planes. Coecients de Newton. Contribution a l'etude des singularites du poit du vue du polygone de Newton. Paris VII, Janvier 1973, These d'Etat. See also in Travaux en Cours, 36 (edit. Le Dung Trang) Introduction a la theorie des singularites I , 49-124, 1988.pl_PL

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