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H 1 Cayley-Bacharach theorems with excess vanishing

Auteurs : Lazarsfeld, Robert (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : A classical result usually attributed to Cayley and Bacharach asserts that if two plane curves of degrees c and d meet in cd points, then any curve of degree (c + d - 3) passing through all but one of these points must also pass through the remaining one. In the late 1970s, Griffiths and Harris showed that this is a special case of a general result about zero-loci of sections of a vector bundle. Inspired by a recent paper of Mu-Lin Li, I will describe a generalization allowing for excess vanishing. Multiplier ideals enter the picture in a natural way. Time permitting, I will also explain how a result due to Tan and Viehweg leads to statements of Cayley-Bacharach type for determinantal loci. This is joint work with Lawrence Ein.

    Keywords : Cayley-Bacharach theorem; multiplier ideals

    Codes MSC :
    14F05 - Sheaves, derived categories of sheaves and related constructions

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 21/10/2019
      Date de captation : 30/09/2019
      Collection : Research talks ; Algebra ; Algebraic and Complex Geometry
      Format : MP4
      Durée : 01:09:46
      Domaine : Algebraic & Complex Geometry ; Algebra
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-09-30_Lazarsfeld.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.19565703
    Cite this video as: Lazarsfeld, Robert (2019). Cayley-Bacharach theorems with excess vanishing. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19565703
    URI : http://dx.doi.org/10.24350/CIRM.V.19565703


    Voir aussi

    Bibliographie

    1. EIN, Lawrence et LAZARSFELD, Robert. Cayley-Bacharach theorems with excess vanishing. arXiv preprint arXiv:1909.08493, 2019. - https://arxiv.org/abs/1909.08493

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