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H 1 A computational approach to Milnor fiber cohomology

Auteurs : Dimca, Alexandru (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : In this talk we consider the Milnor fiber F associated to a reduced projective plane curve $C$. A computational approach for the determination of the characteristic polynomial of the monodromy action on the first cohomology group of $F$, also known as the Alexander polynomial of the curve $C$, is presented. This leads to an effective algorithm to detect all the roots of the Alexander polynomial and, in many cases, explicit bases for the monodromy eigenspaces in terms of polynomial differential forms. The case of line arrangements, where there are many open questions, will illustrate the complexity of the problem. These results are based on joint work with Morihiko Saito, and with Gabriel Sticlaru.

    Keywords : plane curve; Milnor fiber; monodromy

    Codes MSC :
    32S22 - Relations with arrangements of hyperplanes
    32S35 - Mixed Hodge theory of singular varieties
    32S55 - Milnor fibration; relations with knot theory

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 17/06/16
      Date de captation : 31/05/2016
      Collection : Research talks ; Algebraic and Complex Geometry
      Format : MP4
      Durée : 00:55:05
      Domaine : Algebraic & Complex Geometry
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2016-05-31_Dimca.mp4

    Informations sur la rencontre

    Nom de la rencontre : Topology of complex algebraic varieties / Topologie des variétés algébriques complexes
    Organisateurs de la rencontre : Eyssidieux, Philippe ; Klinger, Bruno ; Kotschick, Dieter ; Toledo, Domingo
    Dates : 30/05/2016 - 03/06/2016
    Année de la rencontre : 2016
    URL Congrès : http://conferences.cirm-math.fr/1398.html

    Citation Data

    DOI : 10.24350/CIRM.V.18990103
    Cite this video as: Dimca, Alexandru (2016). A computational approach to Milnor fiber cohomology. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18990103
    URI : http://dx.doi.org/10.24350/CIRM.V.18990103


    Voir aussi

    Bibliographie

    1. Dimca, A., & Sticlaru, G. (2016). A computational approach to Milnor fiber cohomology. - http://arxiv.org/abs/1602.03496

    2. Dimca, A., & Saito, M. (2014). Koszul complexes and spectra of projective hypersurfaces with isolated singularities. - http://arxiv.org/abs/1212.1081

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