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arXiv · 2005.03983

Rigidity of rationally connected smooth projective varieties from dynamical viewpoints

Sheng Meng·Guolei Zhong
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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 $f^*|_{\text{N}^1(X)}$ (without counting multiplicities) are $n$ distinct real numbers greater than $1$.

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Sheng Meng, Guolei Zhong. 2020-05-08. Rigidity of rationally connected smooth projective varieties from dynamical viewpoints. https://doi.org/10.4310/mrl.2023.v30.n2.a10

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