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H 1 Stabilisation in algebraic geometry

Auteurs : Draisma, Jan (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Across many mathematical disciplines one encounters projective systems of algebraic varieties indexed by a combinatorial datum, such as a natural number, a finite graph, or a lattice polytope. As the datum grows, the algebraic complexity of the corresponding variety (measured, for instance, in terms of its defining equations or higher-order syzygies) typically increases. But in good cases it eventually stabilises in a well-defined manner, especially when the family admits a direct system of sufficiently large symmetry groups. Exactly when this stabilisation phenomenon can be expected is still poorly understood, and this question motivates much current research activity in algebraic geometry and adjacent branches. After a brief general setup, which involves passing to the projective limit of the varieties and the direct limit of their symmetry groups, I will discuss a number of concrete instances where stabilisation occurs, both from classical algebraic geometry and from other areas of mathematics.

    Codes MSC :
    14L24 - Geometric invariant theory of group schemes
    14L30 - Group actions on varieties or schemes (quotients)

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 08/04/15
      Date de captation : 24/03/15
      Collection : Research talks ; Algebraic and Complex Geometry
      Format : quicktime ; audio/x-aac
      Durée : 01:02:46
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-03-24_Draisma.mp4

    Informations sur la rencontre

    Nom de la rencontre : Jean Morlet Chair: Artin approximation and Infinite Dimensional Geometry / Chaire Jean Morlet : approximation de Artin et géométrie en dimension infinie
    Organisateurs de la rencontre : Hauser, Herwig ; Rond, Guillaume
    Dates : 23/03/15 - 27/03/15
    Année de la rencontre : 2015
    URL Congrès : http://hauser-rond.weebly.com/main-conference.html

    Citation Data

    DOI : 10.24350/CIRM.V.18737903
    Cite this video as: Draisma, Jan (2015). Stabilisation in algebraic geometry. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18737903
    URI : http://dx.doi.org/10.24350/CIRM.V.18737903


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