Equidistribution in higher codimension for holomorphic endomorphisms of ℙ^{𝕜}

Ahn, Taeyong

doi:10.1090/tran/6539

Equidistribution in higher codimension for holomorphic endomorphisms of $\mathbb {P}^k$
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Abstract:

In this paper, we discuss the equidistribution phenomena for holomorphic endomorphisms over $\mathbb {P}^k$ in the case of bidegree $(p,p)$ with $1\leq p\leq k$, in particular, $1<p<k$. 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 $d^{-pn}(f^n)^*(S)$ converges to $T^p$ exponentially fast in the current sense for every positive closed $(p,p)$-current $S$ of mass $1$ which is smooth on $E$.

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