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arXiv · 1502.02167

Birational splitting and algebraic group actions

Vladimir L. Popov
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Abstract

According to the classical theorem, every irreducible algebraic variety endowed with a nontrivial rational action of a connected linear algebraic group is birationally isomorphic to a product of another algebraic variety and ${\bf P}^s$ with positive $s$. We show that the classical proof of this theorem actually works only in characteristic $0$ and we give a characteristic free proof of it. To this end we prove and use a characterization of connected linear algebraic groups $G$ with the property that every rational action of $G$ on an irreducible algebraic variety is birationally equivalent to a regular action of $G$ on an affine algebraic variety.

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Vladimir L. Popov. 2015-02-07. Birational splitting and algebraic group actions. https://doi.org/10.1007/s40879-015-0050-8

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