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Mathematical Research Letters
Volume 30 (2023)
Number 2
Rigidity of rationally connected smooth projective varieties from dynamical viewpoints
Pages: 589 – 610
DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n2.a10
Authors
Abstract
Let $X$ be a rationally connected smooth projective variety of dimension $n$. We show that $X$ is a toric variety if and only if $X$ admits an int-amplified endomorphism with totally invariant ramification divisor. We also show that $X \cong (\mathbb{P}^1)^{\times n}$ if and only if $X$ admits a surjective endomorphism $f$ such that the eigenvalues of $f^\ast \vert_{\mathrm{N}^1(X)}$ (without counting multiplicities) are $n$ distinct real numbers greater than $1$.
Received 26 February 2021
Received revised 23 October 2021
Accepted 8 November 2021
Published 13 September 2023