Free divisors in prehomogeneous vector spaces

TitreFree divisors in prehomogeneous vector spaces
Type de publicationArticle de revue
AuteurGranger, Jean-Michel , Mond, David, Schulze, Mathias
PaysRoyaume-Uni
EditeurCambridge University Press
VilleCambridge
TypeArticle scientifique dans une revue à comité de lecture
Année2011
LangueAnglais
Date2011/01/05
Numéro5
Pagination923 - 950
Volume102
Titre de la revueProceedings of the London Mathematical Society
ISSN1460-244X
Résumé en anglais

We study linear free divisors, that is, free divisors arising as discriminants in prehomogeneous vector spaces, and in particular in quiver representation spaces. We give a characterization of the prehomogeneous vector spaces containing such linear free divisors. For reductive linear free divisors, we prove that the numbers of geometric- and representation-theoretic irreducible components coincide. As a consequence, we find that a quiver can only give rise to a linear free divisor if it has no (oriented or unoriented) cycles. We also deduce that the linear free divisors which appear in Sato and Kimura's list of irreducible prehomogeneous vector spaces are the only irreducible reductive linear free divisors. Furthermore, we show that all quiver linear free divisors are strongly Euler homogeneous, that they are locally weakly quasihomogeneous at points whose corresponding representation is not regular, and that all tame quiver linear free divisors are locally weakly quasihomogeneous. In particular, the latter satisfy the logarithmic comparison theorem.

URL de la noticehttp://okina.univ-angers.fr/publications/ua132
DOI10.1112/plms/pdq046
Lien vers le document

http://dx.doi.org/10.1112/plms/pdq046