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arXiv · 2308.12096

On conjugacy of additive actions in the affine Cremona group

Ivan Arzhantsev
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Abstract

An additive action on an irreducible algebraic variety $X$ is an effective action $\mathbb{G}_a^n\times X\to X$ with an open orbit of the vector group $\mathbb{G}_a^n$. 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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Ivan Arzhantsev. 2023-08-23. On conjugacy of additive actions in the affine Cremona group. https://doi.org/10.2989/16073606.2024.2344039

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