Linear free divisors and quiver representations

Details Linear free divisors and quiver representations Linear free divisors and quiver representations

2005-09-09

arxiv.org/abs/math/0509221v1

Mathematics

Algebraic Geometry

27 pages; to appear in Singularities and Computer Algebra, papers in honour of G.-M.Greuel's 60th birthday

Scientific paper

Linear free divisors are free divisors, in the sense of K.Saito, with linear presentation matrix (example: normal crossing divisors). Using techniques of deformation theory on representations of quivers, we exhibit families of linear free divisors as discriminants in representation spaces for real Schur roots of a finite quiver. We review some basic material on quiver representations, and explain in detail how to verify whether the discriminant is a free divisor and how to determine its components and their equations, using techniques of A. Schofield. As an illustration, the linear free divisors that arise as the discriminant from the highest roots of Dynkin quivers of type E7 and E8 are treated explicitly.

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