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A birational invariant for algebraic group actions

Zinovy Reichstein·Boris Youssin
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Abstract

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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Zinovy Reichstein, Boris Youssin. 2000-07-28. A birational invariant for algebraic group actions. https://arxiv.org/abs/math/0007181

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