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1972•Mathematics of the USSR-IzvestiyaRequires access

ON THE STABILITY OF THE ACTION OF AN ALGEBRAIC GROUP ON AN ALGEBRAIC VARIETY

Vladimir L. Popov

Open publisher page 42 citations

Abstract

We prove the following fact: if a connected algebraic group having no rational characters acts regularly on a normal irreducible algebraic variety with periodic divisor class group , then for the orbit of a point in general position to be closed, it is sufficient that be an affine variety; moreover, if is affine, this condition is also sufficient.

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What this paper is about

We prove the following fact: if a connected algebraic group having no rational characters acts regularly on a normal irreducible algebraic variety with periodic divisor class group , then for the orbit of a point in general position to be closed, it is sufficient that be an affine variety; moreover, if is affine, this condition is also sufficient.

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OpenAlex reports 42 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We prove the following fact: if a connected algebraic group having no rational characters acts regularly on a normal irreducible algebraic variety with periodic divisor class group , then for the orbit of a point in general position to be closed, it is sufficient that be an affine variety; moreover, if is affine, this condition is also sufficient.

Key concepts: Algebraic group, Singular point of an algebraic variety, Dimension of an algebraic variety, Algebraic cycle, Mathematics, Function field of an algebraic variety, Affine variety, Algebraic surface

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