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The Zariski problem for homogeneous and quasi-homogeneous curves
Multi angle
Authors : Genzmer, Yohann (Author of the conference)
CIRM (Publisher )
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
CIRM (Publisher )
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Abstract :
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
MSC Codes : O. Zariski - analytic classification - foliation - germ - Puiseux expansion
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
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 17/02/15 Conference Date : 04/02/15 Subseries : Research talks arXiv category : Dynamical Systems ; Algebraic Geometry Mathematical Area(s) : Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 01:06:55 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2015-02-04_Genzmer.mp4 
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Information on the Event
Event Title : Applications of Artin approximation in singularity theory / Applications de l'approximation de Artin en théorie des singularitésEvent Organizers : Hauser, Herwig ; Rond, Guillaume Dates : 02/02/15 - 06/02/15 Event Year : 2015 Event URL : https://conferences.cirm-math.fr/1474.html
Citation Data
DOI : 10.24350/CIRM.V.18694303Cite 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 |
Bibliography
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- [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] 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] 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] 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
