m
• E

F Nous contacter

0

Multi angle

H 1 A computational approach to Milnor fiber cohomology

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

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 complexesOrganisateurs de la rencontre : Eyssidieux, Philippe ; Klinger, Bruno ; Kotschick, Dieter ; Toledo, DomingoDates : 30/05/2016 - 03/06/2016 Année de la rencontre : 2016 URL Congrès : http://conferences.cirm-math.fr/1398.htmlCitation 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

Titres de périodiques et e-books électroniques (Depuis le CIRM)

Ressources Electroniques

Books & Print journals

Recherche avancée

0
Z