2005/09/09 by Ragnar-Olaf Buchweitz, David Mond, Buchweitz, Ragnar-Olaf +1 · 1 citation
Mathematics · #14D15 #16G20 #58K60 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14D15 #msc:16G20 #msc:58K60
paper · pdf · doi:10.48550/arxiv.math/0509221
27 pages; to appear in Singularities and Computer Algebra, papers in honour of G.-M.Greuel's 60th birthday
arxiv created 2005/09/09 · openalex publication_date 2005/09/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.