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H 2 Indices of vector fields on singular varieties and the Milnor number

Auteurs : Seade, José (Auteur de la Conférence)
CIRM (Editeur )

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Milnor fibration indices of vector fields Schwartz index GSV index Lê numbers and cycles Chern classes Fulton-Johnson classes Schwartz classes Milnor classes Questions

Résumé : Let $(V,p)$ be a complex isolated complete intersection singularity germ (an ICIS). It is well-known that its Milnor number $\mu$ can be expressed as the difference:
$$\mu = (-1)^n ({\rm Ind}_{GSV}(v;V) - {\rm Ind}_{rad}(v;V)) \;,$$
where $v$ is a continuous vector field on $V$ with an isolated singularity at $p$, the first of these indices is the GSV index and the latter is the Schwartz (or radial) index. This is independent of the choice of $v$.
In this talk we will review how this formula extends to compact varieties with non-isolated singularities. This depends on two different ways of extending the notion of Chern classes to singular varieties. On elf these are the Fulton-Johnson classes, whose 0-degree term coincides with the total GSV-Index, while the others are the Schwartz-McPherson classes, whose 0-degree term is the total radial index, and it coincides with the Euler characteristic. This yields to the well known notion of Milnor classes, which extend the Milnor number. We will discuss some geometric facts about the Milnor classes.

Codes MSC :
14B05 - Singularities
32S65 - Singularities of holomorphic vector fields and foliations
57R20 - Characteristic classes and numbers

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 11/03/15
    Date de captation : 26/02/15
    Collection : Research talks ; Algebraic and Complex Geometry
    Format : QuickTime (.mov) Durée : 00:51:45
    Domaine : Algebraic & Complex Geometry
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2015-02-26_Seade.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.18707003
Cite this video as: Seade, José (2015). Indices of vector fields on singular varieties and the Milnor number. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18707003
URI : http://dx.doi.org/10.24350/CIRM.V.18707003

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