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A birational
invariant for algebraic group actions
Z. Reichstein and B. Youssin |
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Vol. 204 (2002), No. 1, 223–246
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Abstract |
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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. |
Milestones
Received: 13 July 2000
Revised: 16 February 2001
Published: 1 May 2002
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Authors |
| Z. Reichstein | |
| Department of Mathematics Oregon State University Corvallis, OR 97331 |
Department of Mathematics University of British Columbia Vancouver, B.C., Canada V6T 1Z2 |
| B. Youssin | |
| Department of Mathematics and
Computer Science University of the Negev Be’er Sheva’, Israel |
Hashofar 26/3 Ma’ale Adumim, Israel |
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