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H 2 The Zariski problem for homogeneous and quasi-homogeneous curves

Auteurs : Genzmer, Yohann (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The Zariski problem concerns the analytical classification of germs of curves of the complex plane $\mathbb{C}^2$. In full generality, it is asked to understand as accurately as possible the quotient $\mathfrak{M}(f_0)$ of the topological class of the germ of curve $\lbrace f_0(x, y) = 0 \rbrace$ up to analytical equivalence relation. The aim of the talk is to review, as far as possible, the approach of Zariski as well as the recent developments. (Full abstract in attachment).

    O. Zariski - analytic classification - foliation - germ - Puiseux expansion

    Codes MSC :
    32G13 - Analytic moduli problems [For algebraic moduli problems, see 14D20, 14D22, 14H10, 14J10] [See also 14H15, 14J15]
    32S65 - Singularities of holomorphic vector fields and foliations

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 17/02/15
      Date de captation : 04/02/15
      Collection : Research talks ; Algebraic and Complex Geometry
      Format : quicktime ; audio/x-aac
      Durée : 01:06:55
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-02-04_Genzmer.mp4

    Informations sur la rencontre

    Nom de la rencontre : Applications of Artin approximation in singularity theory / Applications de l'approximation de Artin en théorie des singularités
    Organisateurs de la rencontre : Hauser, Herwig ; Rond, Guillaume
    Dates : 02/02/15 - 06/02/15
    Année de la rencontre : 2015
    URL Congrès : https://conferences.cirm-math.fr/1474.html

    Citation Data

    DOI : 10.24350/CIRM.V.18694303
    Cite this video as: Genzmer, Yohann (2015). The Zariski problem for homogeneous and quasi-homogeneous curves. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18694303
    URI : http://dx.doi.org/10.24350/CIRM.V.18694303


    Bibliographie

    1. [1] Hefez, A., & Hernandes, M.E. (2009). Analytic classification of plane branches up to multiplicity 4. Journal of Symbolic Computation, 44(6), 626-634 - http://dx.doi.org/10.1016/j.jsc.2008.09.003

    2. [2] Hefez, A., & Hernandes, M.E. (2011). The analytic classification of plane branches. Bulletin of the London Mathematical Society, 43(2), 289-298 - http://dx.doi.org/10.1112/blms/bdq113

    3. [3] Hefez, A., & Hernandes, M.E. (2013). Algorithms for the implementation of the analytic classification of plane branches. Journal of Symbolic Computation, 50, 308-313 - http://dx.doi.org/10.1016/j.jsc.2012.08.003

    4. [4] Mattei, J.-F. (1991). Modules de feuilletages holomorphes singuliers. I: équisingularité. Inventiones Mathematicae 103(2), 297-325 - http://dx.doi.org/10.1007/BF01239515

    5. [5] Zariski, O. (1986). Le problème des modules pour les branches planes : cours donné au Centre de mathématiques de l'École polytechnique. Paris: Hermann - https://www.zbmath.org/?q=an:0592.14010

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