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H 1 Symplectic singularities of varieties

Auteurs : Domitrz, Wojciech (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We study germs of singular varieties in a symplectic space. We introduce the algebraic restrictions of differential forms to singular varieties and prove the generalization of Darboux-Givental' theorem from smooth submanifolds to arbitrary quasi-homogeneous varieties in a symplectic space. Using algebraic restrictions we introduce new symplectic invariants and explain their geometric meaning. We show that a quasi-homogeneous variety $N$ is contained in a non-singular Lagrangian submanifold if and only if the algebraic restriction of the symplectic form to $N$ vanishes. The method of algebraic restriction is a powerful tool for various classification problems in a symplectic space. We illustrate this by the construction of a complete system of invariants in the problem of classifying singularities of immersed $k$-dimensional submanifolds of a symplectic 2n-manifold at a generic double point.

    Keywords: symplectic manifolds - symplectic multiplicity and other invariants - Darboux-Givental's theorem - quasi-homogeneous singularities - singularities of planar curves

    Codes MSC :
    32S25 - Surface and hypersurface singularities [See also 14J17]
    53D05 - Symplectic manifolds
    58K55 - Asymptotic behavior

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 16/03/15
      Date de captation : 05/03/15
      Collection : Research talks ; Algebraic and Complex Geometry
      Format : quicktime ; audio/x-aac
      Durée : 00:53:38
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-03-05_Domitrz.mp4

    Informations sur la rencontre

    Nom de la rencontre : Geometry of singular spaces and maps / Géométrie des espaces et applications singuliers
    Organisateurs de la rencontre : Brasselet, Jean-Paul ; Pichon, Anne
    Dates : 02/03/15 - 06/03/15
    Année de la rencontre : 2015
    URL Congrès : https://conferences.cirm-math.fr/1478.html

    Citation Data

    DOI : 10.24350/CIRM.V.18719503
    Cite this video as: Domitrz, Wojciech (2015). Symplectic singularities of varieties. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18719503
    URI : http://dx.doi.org/10.24350/CIRM.V.18719503


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