Free divisors in prehomogeneous vector spaces
Granger, Michel, Mond, D. (David) and Schulze, Mathias. (2011) Free divisors in prehomogeneous vector spaces. Proceedings of the London Mathematical Society, Volume 102 (Number 5). pp. 923-950. ISSN 0024-6115Full text not available from this repository.
Official URL: http://dx.doi.org/10.1112/plms/pdq046
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|
|Library of Congress Subject Headings (LCSH):||Vector spaces , Invariants|
|Journal or Publication Title:||Proceedings of the London Mathematical Society|
|Publisher:||London Mathematical Society|
|Official Date:||May 2011|
|Page Range:||pp. 923-950|
1. M. Auslander, I. Reiten and S. O. Smalø, Representation theory of Artin algebras, Cambridge Studies
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