Research Article

On conjugacy of additive actions in the affine Cremona group

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

DOI: 10.2989/16073606.2024.2344039

Author(s): Ivan ArzhantsevHSE 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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Research Article

On conjugacy of additive actions in the affine Cremona group

Abstract

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