Freeness of hyperplane arrangements and related topics

Yoshinaga, Masahiko

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Numéro Spécial à l’occasion de la conférence Arrangements in Pyrénées, Pau 11-15 juin 2012, Tome 23 (2014) no. 2, pp. 483-512.

Cet article est un développement des notes de l’exposé donnée par l’auteur à la conférence « Arrangements en Pyrénées », en juin 2012. Nous discutons les relations entre les problèmes de liberté et ceux de décomposabilité pour les fibrés vectoriels, plusieurs techniques qui prouvent la liberté pour des arrangements d’hyperplans, la théorie de K. Saito des dérivations primitives pour les arrangements de Coxeter, leur application à des problèmes combinatoires et quelques conjectures liées.

These are the expanded notes of the lecture by the author in “Arrangements in Pyrénées”, June 2012. We are discussing relations of freeness and splitting problems of vector bundles, several techniques proving freeness of hyperplane arrangements, K. Saito’s theory of primitive derivations for Coxeter arrangements, their application to combinatorial problems and related conjectures.

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