The second main theorem with moving hypersurfaces in subgeneral position

Qili Cai; Chin-Jui Yang; Qili Cai; Chin-Jui Yang

doi:10.3934/math.2025404

AIMS Mathematics

2025, Volume 10, Issue 4: 8818-8826. doi: 10.3934/math.2025404

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The second main theorem with moving hypersurfaces in subgeneral position

Qili Cai ^,,
Chin-Jui Yang ^{2
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1.
School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou, 510665, China
2.
Department of Mathematics, University of Houston, Houston, TX 77204, USA

Received: 23 November 2024 Revised: 02 April 2025 Accepted: 02 April 2025 Published: 17 April 2025
MSC : 32A22, 32H30

In this paper, we prove a second main theorem for a holomorphic curve $ f $ into $ \mathbb P^N (\mathbb C) $ with a family of slowly moving hypersurfaces $ D_1, ..., D_q $ with respect to $ f $ in $ m $-subgeneral position, proving an inequality with factor $ 3 \over 2 $. The motivation comes from the recent result of Heier and Levin.
- Nevanlinna theory,
- homolorphic curves,
- second main theorem,
- moving targets,
- distributive constants
Citation: Qili Cai, Chin-Jui Yang. The second main theorem with moving hypersurfaces in subgeneral position[J]. AIMS Mathematics, 2025, 10(4): 8818-8826. doi: 10.3934/math.2025404

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Abstract

In this paper, we prove a second main theorem for a holomorphic curve $ f $ into $ \mathbb P^N (\mathbb C) $ with a family of slowly moving hypersurfaces $ D_1, ..., D_q $ with respect to $ f $ in $ m $-subgeneral position, proving an inequality with factor $ 3 \over 2 $. The motivation comes from the recent result of Heier and Levin.

References

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