AI 中文总结
针对光滑射影簇的内放大自同态，证明其完全不变素环的总次数满足显式希尔伯特函数界，且在射影空间情形下得到最优的素环数量组合数界。
AI 中文摘要
设X为光滑射影簇，f:X→X为内放大自同态，L为X上任意丰富线丛。我们证明，在每个余维下，经f迭代后成为完全不变的素环的总次数，满足其总L次数的显式希尔伯特函数界。特别地，当X=Pⁿ时，完全不变素(n-r)环的数量以组合数(n+1 r)为界，且该界是最优的。
英文摘要
Let $X$ be a smooth projective variety, $f:X\to X$ an int-amplified endomorphism, and $L$ any ample line bundle on $X$. We prove that, in every codimension, the total degree of prime cycles that become totally invariant under an iterate of $f$ satisfies an explicit Hilbert-function bound on their total $L$-degree. In particular, when $X=\mathbf{P}^n$, the number of totally invariant prime $(n-r)$-cycle is bounded by $\binom{n+1}{r}$, and this bound is optimal.
Comments18 pages, updated fundings
