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H 1 Group actions on quiver moduli spaces and applications

Auteurs : Hoskins, Victoria (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We study two types of actions on King’s moduli spaces of quiver representations over a field k, and we decompose their fixed loci using group cohomology in order to give modular interpretations of the components. The first type of action arises by considering finite groups of quiver automorphisms. The second is the absolute Galois group of a perfect field k acting on the points of this quiver moduli space valued in an algebraic closure of k; the fixed locus is the set of k-rational points, which we decompose using the Brauer group of k, and we describe the rational points as quiver representations over central division algebras over k. Over the field of complex numbers, we describe the symplectic and holomorphic geometry of these fixed loci in hyperkaehler quiver varieties using the language of branes. Over the reals, the rational points of these quiver moduli spaces come from either real or quaternionic quiver representations, and we compute the Poincaré polynomials of both components.
    This is joint work with Florent Schaffhauser.

    Codes MSC :
    14D20 - Algebraic moduli problems, moduli of vector bundles
    14L24 - Geometric invariant theory

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 20/12/2017
      Date de captation : 14/12/2017
      Collection : Research talks
      Format : MP4
      Durée : 00:54:19
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2017-12-14_Hoskins.mp4

    Informations sur la rencontre

    Nom du congrès : Algebraic geometry and complex geometry / Géométrie algébrique et géométrie complexe
    Organisteurs Congrès : Broustet, Amaël ; Pasquier, Boris
    Dates : 11/12/2017 - 15/12/2017
    Année de la rencontre : 2017
    URL Congrès : https://conferences.cirm-math.fr/1692.html

    Citation Data

    DOI : 10.24350/CIRM.V.19257903
    Cite this video as: Hoskins, Victoria (2017). Group actions on quiver moduli spaces and applications. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19257903
    URI : http://dx.doi.org/10.24350/CIRM.V.19257903


    Voir aussi

    Bibliographie

    1. Hoskins, V., & Schaffhauser, F. (2017). Group actions on quiver varieties and applications. - https://arxiv.org/abs/1612.06593

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