dc.contributor.author | Barroso, Evelia Rosa Garcia | |
dc.contributor.author | Płoski, Arkadiusz | |
dc.contributor.editor | Krasiński, Tadeusz | |
dc.contributor.editor | Spodzieja, Stanisław | |
dc.date.accessioned | 2020-01-28T12:05:06Z | |
dc.date.available | 2020-01-28T12:05:06Z | |
dc.date.issued | 2019 | |
dc.identifier.citation | García 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.identifier.uri | http://hdl.handle.net/11089/31339 | |
dc.description.abstract | We 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.language.iso | en | pl_PL |
dc.publisher | Wydawnictwo Uniwersytetu Łódzkiego | pl_PL |
dc.relation.ispartof | Analytic and Algebraic Geometry 3; | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.title | Contact exponent and the Milnor number of plane curve singularities | pl_PL |
dc.type | Book chapter | pl_PL |
dc.page.number | 93-109 | pl_PL |
dc.contributor.authorAffiliation | Departamento de Matematicas, Estadistica e I.O. Seccion de Matematicas, Universidad de La Laguna Apartado de Correos 456 | pl_PL |
dc.contributor.authorAffiliation | Department of Mathematics and Physics, Kielce University of Technology | pl_PL |
dc.references | Angerm uller, G. Die Wertehalbgruppe einer ebener irreduziblen algebroiden Kurve. Math. Z. 153 (1977), no. 3, 267-282. | pl_PL |
dc.references | Brieskorn, E. and H. Knorrer. Plane algebraic curves. Birkh auser Verlag 1986. | pl_PL |
dc.references | Campillo, A. Algebroid curves in positive characteristic. Lecture Notes in Mathematics, 813. Springer Verlag, Berlin, 1980. v+168 pp. | pl_PL |
dc.references | Eggers, H. Polarinvarianten und die Topologie von Kurvensingularit aten. Bonner Mathematische Schriften, Vol. 147, 1983. | pl_PL |
dc.references | Garcia 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.references | Garcia 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.references | Garcia Barroso, E. and A. Płoski. An approach to plane algebroid branches. Rev. Mat. Complut., 28 (1) (2015), 227-252. | pl_PL |
dc.references | Garcia 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.references | Gwoździewicz, 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.references | Hironaka, H. Introduction to the theory of in nitely near singular points, Memorias del Instituto Jorge Juan 28, Madrid 1974. | pl_PL |
dc.references | Melle-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.references | Lejeune-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 |
dc.contributor.authorEmail | ergarcia@ull.es | pl_PL |
dc.contributor.authorEmail | matap@tu.kielce.pl | pl_PL |