A birational invariant for algebraic group actions

Details A birational invariant for algebraic group actions A birational invariant for algebraic group actions

2000-07-28

arxiv.org/abs/math/0007181v1

Mathematics

Algebraic Geometry

23 pages, AMS LaTEX 1.1. Author-supplied dvi file available at http://ucs.orst.edu/~reichstz/pub.html

Scientific paper

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 PGL_n-varieties.

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