Rigidity of rationally connected smooth projective varieties from dynamical viewpoints

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 $f^{\ast }{|}_{{\text{N}}^1(X)}$ (without counting multiplicities) are $n$ distinct real numbers greater than $1$.

Minor revision. Final version

References in corpus (2)

• Questions on self maps of algebraic varieties
• Amplified endomorphisms of Fano fourfolds

Cited by in corpus (4)

• Invariant subvarieties with small dynamical degree
• Amplified endomorphisms of Fano fourfolds
• Boundedness of finite morphisms onto Fano manifolds with large Fano index
• Advances in the equivariant minimal model program and their applications in complex and arithmetic dynamics