$\mathbb{P}^k$的全纯自同态在高余维上的等分布
Equidistribution in Higher Codimension for Holomorphic Endomorphisms of $\mathbb{P}^k$
摘要：
本文讨论了在二次$(p,p)$有$1<p<k$的情况下，$\mathbb{P}^k$上全纯自同态的等分布现象.证明了如果$f:\mathbb{P}^k\to\mathbb{P}^k$是一个全纯自同态的程度$d\geq 2$和$T^p$表示绿色$(p,p)$ -电流与$f$，则存在一个适当的不变的分析子集$E$ $f$，使$d^{-pn}(f^n)^*(S)\to T^p$指数快速在当前意义下，对每个正封闭的$(p,p)$ -电流$S$的质量为1，使$S$是光滑的$E$。
英文摘要：
In this paper, we discuss the equidistribution phenomena for holomorphic endomorphisms over $\mathbb{P}^k$ in the case of bidegree $(p,p)$ with $1<p<k$. We prove that if $f:\mathbb{P}^k\to\mathbb{P}^k$ is a holomorphic endomorphism of degree $d\geq 2$ and $T^p$ denotes the Green $(p,p)$-current associated with $f$, then there exists a proper invariant analytic subset $E$ for $f$ such that $d^{-pn}(f^n)^*(S)\to T^p$ exponentially fast in the current sense for every positive closed $(p,p)$-current $S$ of mass 1 such that $S$ is smooth on $E$.
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