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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.02458 |
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Table of Contents:
- We study birational automorphisms of algebraic varieties of bounded growth, i.e. such that the norms of the inverse images ${(f^n)}^* \colon \mathrm{NS}(X)\to \mathrm{NS}(X)$ of the powers of the automorphism $f\in\mathrm{Bir}(X)$ are bounded above for $n\geqslant 0$. We prove that some power of an infinite order automorphism of a variety $X$ with such property factors either through an infinite order translation on the Albanese variety of $X$ or through an infinite order regular automorphism of $\mathbb{P}^m$ for $m\geqslant 1$. We deduce from this that if a rationally connected threefold admits an infinite order automorphism whose growth is bounded then the threefold is rational and an iterate of the automorphism is birationally conjugate to a regular automorphism of $\mathbb{P}^3$, a generalization of Blanc and Deserti's result.