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H 1 Special rational fibrations in Fano 4-folds

Auteurs : Casagrande, Cinzia (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Smooth, complex Fano 4-folds are not classified, and we still lack a good understanding of their general properties. We focus on Fano 4-folds with large second Betti number $b_{2}$, studied via birational geometry and the detailed analysis of their contractions and rational contractions (we recall that a contraction is a morphism with connected fibers onto a normal projective variety, and a rational contraction is given by a sequence of flips followed by a contraction). The main result that we want to present is the following: let $X$ be a Fano 4-fold having a nonconstant rational contraction $X --> Y$ of fiber type. Then either $b_{2}(X)$ is at most 18, with equality only for a product of surfaces, or $Y$ is $\mathbb{P}^{1}$ or $\mathbb{P}^{2}$. The proof is achieved by reducing to the case of "special" rational contractions of fiber type. We will explain this notion and give an idea of the techniques that are used.

    Keywords : Fano varieties; 4-folds; birational geometry

    Codes MSC :
    14E30 - Minimal model program (Mori theory, extremal rays)
    14J35 - Algebraic $4$-folds
    14J45 - Fano varieties

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 21/10/2019
      Date de captation : 03/10/2019
      Collection : Research talks ; Algebraic and Complex Geometry
      Format : MP4
      Durée : 01:00:50
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-10-03_Casagrande.mp4

    Informations sur la rencontre

    Nom de la rencontre : The Geometry of Algebraic Varieties / Géométrie des variétés algébriques
    Organisateurs de la rencontre : Benoist, Olivier ; Jiang, Zhi ; Voisin, Claire
    Dates : 30/09/2019 - 04/10/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/2069.html

    Citation Data

    DOI : 10.24350/CIRM.V.19565303
    Cite this video as: Casagrande, Cinzia (2019). Special rational fibrations in Fano 4-folds. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19565303
    URI : http://dx.doi.org/10.24350/CIRM.V.19565303

    Voir aussi


    1. CASAGRANDE, Cinzia. Fano 4-folds with rational fibrations. arXiv preprint arXiv:1902.01835, 2019. - https://arxiv.org/abs/1902.01835