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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.00607 |
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| _version_ | 1866929332983693312 |
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| author | Ahn, Taeyong |
| author_facet | Ahn, Taeyong |
| contents | In this paper, we prove that for a given surjective holomorphic endomorphism $f$ of a compact Kähler manifold $X$ and for some integer $p$ with $1\le p\le k$, there exists a proper invariant analytic subset $E$ for $f$ such that if $S$ is smooth in a neighborhood of $E$, the sequence $d_p^{-n}(f^n)^*(S-α_S)$ converges to $0$ exponentially fast in the sense of currents where $d_p$ denotes the dynamical degree of order $p$ and $α_S$ is a closed smooth form in the de Rham cohomology class of $S$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_00607 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverse images of a positive closed current for a holomorphic endomorphism of a compact Kähler manifold Ahn, Taeyong Complex Variables Dynamical Systems In this paper, we prove that for a given surjective holomorphic endomorphism $f$ of a compact Kähler manifold $X$ and for some integer $p$ with $1\le p\le k$, there exists a proper invariant analytic subset $E$ for $f$ such that if $S$ is smooth in a neighborhood of $E$, the sequence $d_p^{-n}(f^n)^*(S-α_S)$ converges to $0$ exponentially fast in the sense of currents where $d_p$ denotes the dynamical degree of order $p$ and $α_S$ is a closed smooth form in the de Rham cohomology class of $S$. |
| title | Inverse images of a positive closed current for a holomorphic endomorphism of a compact Kähler manifold |
| topic | Complex Variables Dynamical Systems |
| url | https://arxiv.org/abs/2405.00607 |