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H 1 The intersection form, logarithmic vector fields, and the Severi strata in the discriminant of a plane curve singularity

Auteurs : Mond, David (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : This talk will describe ongoing joint work with Paul Cadman and Duco van Straten, based on the PhD thesis of the former. Givental and Varchenko used the period mapping to pull back the intersection form on the Milnor fibre of an irreducible plane curve singularity $C$, and thereby define a symplectic structure on the base space of a miniversal deformation. We show how to combine this with a symmetric basis for the module of vector fields tangent to the discriminant, to produce involutive ideals $I_k$ which define the strata of parameter values $u$ such that $\delta(C_u)\leq k$. In the process we find an unexpected Lie algebra and a still mysterious canonical deformation of the module structure of the critical space over the discriminant. Much of this work is experimental - a crucial gap in understanding still needs bridging.

    Codes MSC :
    14H20 - Singularities, local rings [See also 13Hxx, 14B05]
    14H50 - Plane and space curves
    32S30 - Deformations of singularities; vanishing cycles

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 16/03/15
      Date de captation : 03/03/15
      Collection : Algebraic and Complex Geometry
      Sous collection : Research talks
      Format : quicktime ; audio/x-aac
      Domaine : Algebraic & Complex Geometry
      Durée : 00:49:36
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-03-03_Mond.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.18719103
    Cite this video as: Mond, David (2015). The intersection form, logarithmic vector fields, and the Severi strata in the discriminant of a plane curve singularity. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18719103
    URI : http://dx.doi.org/10.24350/CIRM.V.18719103


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