Granger, Michel, Mond, D. (David) and Schulze, Mathias. (2011) Free divisors in prehomogeneous vector spaces. Proceedings of the London Mathematical Society, Vol.102 (No.5). pp. 923-950. ISSN 0024-6115

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Abstract

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Proceedings of the London Mathematical Society
Publisher:	London Mathematical Society
ISSN:	0024-6115
Date:	May 2011
Volume:	Vol.102
Number:	No.5
Page Range:	pp. 923-950
Identification Number:	10.1112/plms/pdq046
Status:	Peer Reviewed
URI:	http://wrap.warwick.ac.uk/id/eprint/34863

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