Research Article

On conjugacy of additive actions in the affine Cremona group

Published in: Quaestiones Mathematicae
Volume 47 , issue 9 , 2024 , pages: 1767–1774

DOI: 10.2989/16073606.2024.2344039

Author(s): Ivan Arzhantsev HSE University, Russia

Keywords: Primary: 14L30 , 14R10 , Secondary: 13E10 , 14E07 , 14J50 , Algebraic variety , projective space , automorphism , birational isomorphism , Cremona group , algebraic group action , local algebra , Hassett-Tschinkel correspondence

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Abstract

An additive action on an irreducible algebraic variety X is an effective action with an open orbit of the vector group . Any two additive actions on X are conjugate by a birational automorphism of X. We prove that, if X is the projective space, the conjugating element can be chosen in the affine Cremona group and it is given by so-called basic polynomials of the corresponding local algebra.

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