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Working paper

Birational splitting and algebraic group actions

arxiv.org. math. Cornell University, 2015. No. 1502.02167.
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 the s-dimensional projectice space 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.