| 韩静,沈稼霁.关于P2(C)全纯曲线唯一性问题的注记*[J].数学年刊A辑,2023,44(3):315~322 |
| 关于P2(C)全纯曲线唯一性问题的注记* |
| A Note on the Unicity of Holomorphic Curves in P2(C) |
| Received:July 26, 2021 Revised:May 05, 2023 |
| DOI：10.16205/j.cnki.cama.2023.0022 |
| 中文关键词: 全纯曲线, 超平面, 第二基本定理, 唯一性问题, 次一般位置 |
| 英文关键词:Holomorphic curve, Hyperplane, Second main theorem, Uniqueness problem, Subgeneral position |
| 基金项目:国家自然科学基金 (No.11971353) |
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| 中文摘要: |
| 本文讨论P2(C)中全纯曲线相交处于次一般位置超平面的唯一性.设f1, f2, · · · , fλ为P2(C)中线性非退化的全纯曲线,H1, H1, · · · , Hq为P2(C)上处于m-次一般位置的超平面,满足Aj :f1-1(Hj) = · · · =fλ-1(Hj) (1 ≤ j ≤ q)且Ai ∩ Aj = ?(i = j).假设存在整数l (2 ≤ l ≤ λ),使得fj1(z) ∧ fj2(z) ∧ · · · ∧ fjl(z) = 0 (z ∈ Aj)对任意l个指标1 ≤ j1 < j2 < · · · < jl < λ成立.那么当 q > 2λ/λ-l+1 + 3/2 m时, f1 ∧ · · · ∧ fλ ≡ 0.关键技术是第二基本定理中不等式改进为: ∥(q - 3m/2)Tft(r)≤ Pjq=1N2(ft,Hj )(r, 0) + o(Tft(r))(1 ≤ t ≤ λ). |
| 英文摘要: |
| In this paper, the unicity of holomorphic curves in P2(C) intersecting hyperplanes in subgeneral position is discussed. Let f1, f2, · · · , fλ be linearly non-degenerate holomorphic curves in P2(C) , and H1, H1, · · · , Hq be hyperplanes in P2(C) located in msubgeneral position such that Aj :f1-1(Hj) = · · · =fλ-1(Hj) (1 ≤ j ≤ q) and Ai ∩ Aj = ? (i = j). Assume that there exists an integer l with 2 ≤ l ≤ λ such that fj1(z) ∧ fj2(z) ∧ · · · ∧ fjl(z) = 0 (z ∈ Aj) for any l indices 1 ≤ j1 < j2 < · · · < jl < λ Then, when q > 2λ/λ-l+1 + 3/2 m, f1 ∧ · · · ∧ fλ ≡ 0.The key technique is an improved second main theorem with inequality ∥(q - 3m/2)Tft(r)≤ Pjq=1N2(ft,Hj )(r, 0) + o(Tft(r))(1 ≤ t ≤ λ). |
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