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arXiv · 2208.06938

Rational self-maps with a regular iterate on a semiabelian variety

Jason Bell·Dragos Ghioca·Zinovy Reichstein
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Abstract

Let $G$ be a semiabelian variety defined over an algebraically closed field $K$ of characteristic $0$. Let $\Phi\colon G\dashrightarrow G$ be a dominant rational self-map. Assume that an iterate $\Phi^m \colon G \to G$ is regular for some $m \geqslant 1$ and that there exists no non-constant homomorphism $\tau: G\to G_0$ of semiabelian varieties such that $\tau\circ \Phi^{m k}=\tau$ for some $k \geqslant 1$. We show that under these assumptions $\Phi$ itself must be a regular. We also prove a variant of this assertion in prime characteristic and present examples showing that our results are sharp.

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Jason Bell, Dragos Ghioca, Zinovy Reichstein. 2022-08-14. Rational self-maps with a regular iterate on a semiabelian variety. https://arxiv.org/abs/2208.06938

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