有理连通光滑射影簇的动力视角刚性
Rigidity of rationally connected smooth projective varieties from dynamical viewpoints
AI总结：
本文从动力系统视角研究了有理连通光滑射影簇的刚性，证明了其成为环面簇或$(\mathbb{P}^1)^{\times n}$的充要条件分别取决于其自同态的分支除子不变性与特征值性质。
摘要：
设$X$为$n$维有理连通光滑射影簇。我们证明$X$是环面簇当且仅当$X$允许具有完全不变分支除子的整放大自同态。我们还证明$X\cong (\mathbb{P}^1)^{\times n}$当且仅当$X$允许满射自同态$f$，使得$f^*|_{\text{N}^1(X)}$的特征值（不计重数）为$n$个大于$1$的不同实数。
英文摘要：
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 $1$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
