2000/07/28 by Zinovy Reichstein, Reichstein, Zinovy, Boris Youssin +1
Mathematics · #14E05 #14E15 #14L30 #16A39 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.AG #math.RA #msc:14E05 #msc:14E15 #msc:14L30 #msc:16A39
paper · pdf · doi:10.48550/arxiv.math/0007181
23 pages, AMS LaTEX 1.1. Author-supplied dvi file available at http://ucs.orst.edu/~reichstz/pub.html
arxiv created 2000/07/28 · openalex publication_date 2000/07/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a birational invariant for certain algebraic group actions. We use this invariant to classify linear representations of finite abelian groups up to birational equivalence, thus answering, in a special case, a question of E. B. Vinberg and giving a family of counterexamples to a related conjecture of P. I. Katsylo. We also give a new proof of a theorem of M. Lorenz on birational equivalence of quantum tori (in a slightly expanded form) by applying our invariant in the setting of PGLn-varieties.