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This article, based on the talk given by one of the authors at the Pierret-tefest in Castro Urdiales in June 2008, is an overview of a number of recent results on the polar invariants of plane curve singularities.
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Tom
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303--323
Opis fizyczny
Bibliogr. 46 poz.
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autor
autor
autor
- Department of Mathematics Technical University Al. 1000 L PP 7 25-314 Kielce, Poland, matjg@tu.kielce.pl
Bibliografia
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- [8] H. Eggers, Polarinvarianten und die Topologie von Kurvensingularitäten, Bonner Math. Schriften 147, Universität Bonn, Bonn 1982.
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- [10] E. García Barroso, Sur les courbes polaires d’une courbe plane réduite, Proc. London Math. Soc. (3), 81 (2000), 1–28.
- [11] E. García Barroso, J. Gwoździewicz, Characterization of jacobian Newton polygons of plane branches and new criteria of irreducibility, arXiv:085.4257 (to appear in Ann. Inst. Fourier (Grenoble) vol. 60 no. 2).
- [12] E. R. García Barroso, T. Krasiński, A. Płoski, The Łojasiewicz numbers and plane curve singularities, Ann. Pol. Math. 87 (2005), 127–150.
- [13] E. R. García Barroso, A. Płoski, Pinceaux de courbes planes et invariants polaires, Ann. Pol. Math. 82 (2004), 113–128.
- [14] E. R. García Barroso, A. Lenarcik, A. Płoski, Characterization of nondegenerate plane curve singularities, Univ. Iagel. Acta Math. 45 (2007), 27–36.
- [15] J. Gwoździewicz, A. Lenarcik, A. Płoski, The jacobian Newton polygon and equisingularity of plane curve singularities (in preparation).
- [16] J. Gwoździewicz, A. Płoski, On the Merle formula for polar invariants, Bull. Soc. Sci. Lett. Łódź 41 (7) (1991), 61–67.
- [17] J. Gwoździewicz, A. Płoski, On the approximate roots of polynomials, Ann. Polon. Math. 3 (1995), 199–210.
- [18] J. Gwoździewicz, A. Płoski, On the polar quotients of an analytic plane curve, Kodai Math. J. 25 (2002), 43–53.
- [19] J. Gwoździewicz, A. Płoski, Łojasiewicz exponents and singularities at infinity of polynomials in two complex variables, Coll. Math. 103 (2005), 47–60.
- [20] S. Izumi, S. Koike, T-Ch. Kuo, Computation and stability of the Fukui Invariant , Compositio Math. 130 (2002), 49–73.
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- [27] D. T. Lê, C. P. Ramanujam, The invariance of Milnor’s number implies the invariance of the topological type, Amer. J. Math. 98 (1976), 67–78.
- [28] A. Lenarcik, A. Płoski, Polar invariants of plane curves and the Newton polygon, Kodai Math. J. 23 (2000), 309–319.
- [29] A. Lenarcik, M. Masternak, A. Płoski, Factorization of the polar curve and the Newton polygon, Kodai Math. J. 26 (2003), 288–303.
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- [31] A. Lenarcik, On the jacobian Newton polygon of plane curve singularities, Manuscripta Math. 125 (2008), 309–324.
- [32] M. Merle, Invariants polaires des courbes planes, Invent. Math. 41 (1977), 103–111.
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- [35] A. Płoski, Polar quotients and singularities at infinity of polynomials in two complex variables, Ann. Polon. Math. 78 (2002), 49–58.
- [36] A. Płoski, On the special values for pencils of plane curve singularities, Univ. Iagel. Acta. Math. 42 (2004), 7–13.
- [37] H. J. S. Smith, On the higher singularities of plane curves, Proc. London Math. Soc. 6 (1875), 153–182.
- [38] B. Teissier, Cycles évanescents, sections planes et conditions de Whitney, Astérisque (Société Mathématique de France), No 7-8, 1973.
- [39] B. Teissier, Introduction to equisingularity problems, Proc. Sym. Pure Math., vol 29 (AMS Providence) RI (1975), 593–632.
- [40] B. Teissier, The hunting of invariants in the geometry of discriminants, Nordic Summer School/NAVF Symposium in Mathematics, Oslo, August 5–25, 1976.
- [41] B. Teissier, Varietés polaires I. Invariants polaires des singularités des hypersurfaces, Invent. Math. 40 (1977), 267–292.
- [42] B. Teissier, Polyèdre de Newton Jacobien et équisingularité, Séminaire sur les Singularités, Publications Math., Université Paris VII, 7 (1980), 193–221, http://pepole.math.jussieu.fr/˜teissier/articles-Teissier.html.
- [43] B. Teissier, Introduction to Curve Singularities, Singularity Theory, Editors D. T. Lê, K. Saito, B. Teissier, Word Scientific 1991.
- [44] C. T. C. Wall, Chains on the Eggers tree and polar curves, Rev. Mat. Ibera 19 (2003), 745–754.
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- [46] O. Zariski, Le problème de modules pour les branches des courbes planes, Lecture Notes (ed. F. Kmety and M. Merle), École Polytechnique, 1973.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA5-0027-0044