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June 2021 Degeneracy and finiteness problems for holomorphic curves from a disc into $\mathbf{P}^n(C)$ with finite growth index
Duc Quang Si
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Kodai Math. J. 44(2): 369-391 (June 2021). DOI: 10.2996/kmj44209

Abstract

Let $f^1,f^2,f^3$ are three holomorphic curves from a complex disc $\Delta (R)$ into $\mathbf{P}^n(\mathbf{C})\ (n\ge 2)$ with finite growth indexes $c_{f^1},c_{f^2},c_{f^3}$ and sharing $q (q \ge 2n+2)$ hyperplanes in general position regardless of multiplicity. In this paper, we will show the above bounds for the sum $c_{f^1}+c_{f^2}+c_{f^3}$ to ensure that $f^1\wedge f^2\wedge f^3=0$ or there are two curves among $\{f^1,f^2,f^3\}$ coincide to each other. Our results are generalizations of the previous degeneracy and finiteness results for linearly non-degenerate meromorphic mappings from $\mathbf{C}^m$ into $\mathbf{P}^n(\mathbf{C})$ sharing $(2n+2)$ hyperplanes regardless of multiplicities.

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Duc Quang Si. "Degeneracy and finiteness problems for holomorphic curves from a disc into $\mathbf{P}^n(C)$ with finite growth index." Kodai Math. J. 44 (2) 369 - 391, June 2021. https://doi.org/10.2996/kmj44209

Information

Received: 30 August 2020; Published: June 2021
First available in Project Euclid: 29 June 2021

Digital Object Identifier: 10.2996/kmj44209

Subjects:
Primary: 32A22, 32H30
Secondary: 30D35

Rights: Copyright © 2021 Tokyo Institute of Technology, Department of Mathematics

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Vol.44 • No. 2 • June 2021
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