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H 1 Grothendieck residue in the Jacobian algebra and cup product in vanishing cohomology

Auteurs : Gómez-Mont, Xavier (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The Jacobian algebra, obtained from the ring of germs of functions modulo the partial derivatives of a function $f$ with an isolated singularity, has a non-degenerate bilinear form, Grothendieck Residue, for which multiplication by $f$ is a symmetric nilpotent operator. The vanishing cohomology of the Milnor Fibre has a bilinear form induced by cup product for which the nilpotent operator $N$, the logarithm of the unipotent part of the monodromy, is antisymmetric. Using the nilpotent operators we obtain primitive parts of the bilinear form and we compare both bilinear forms. In particular, over $\mathbb{R}$, we obtain signatures of these primitive forms, that we compare.

    Codes MSC :
    14B05 - Singularities
    32S55 - Milnor fibration; relations with knot theory
    32S65 - Singularities of holomorphic vector fields and foliations

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 10/03/15
      Date de captation : 24/02/15
      Collection : Algebraic and Complex Geometry
      Sous collection : Research talks
      Format : quicktime ; audio/x-aac
      Domaine : Algebraic & Complex Geometry
      Durée : 00:53:56
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2015-02-24_Gomez_Mont.mp4

    Informations sur la rencontre

    Nom de la rencontre : Local and global invariants of singularities / Invariants locaux et globaux des singularités
    Organisateurs de la rencontre : Dutertre, Nicolas ; Pichon, Anne
    Dates : 23/02/15 - 27/02/15
    Année de la rencontre : 2015
    URL Congrès : http://chairejeanmorlet-1stsemester2015....

    Citation Data

    DOI : 10.24350/CIRM.V.18707203
    Cite this video as: Gómez-Mont, Xavier (2015). Grothendieck residue in the Jacobian algebra and cup product in vanishing cohomology. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18707203
    URI : http://dx.doi.org/10.24350/CIRM.V.18707203


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