Second main theorem for holomorphic curves on annuli with arbitrary families of hypersurfaces

Liu Yang; Yuehuan Zhu; Liu Yang; Yuehuan Zhu

doi:10.3934/era.2024063

Electronic Research Archive

2024, Volume 32, Issue 2: 1365-1379. doi: 10.3934/era.2024063

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Research article

Second main theorem for holomorphic curves on annuli with arbitrary families of hypersurfaces

Liu Yang ^,,
Yuehuan Zhu

Department of Applied Mathematics, Anhui University of Technology, Maanshan 243032, Anhui province, China

Received: 02 October 2023 Revised: 23 December 2023 Accepted: 09 January 2024 Published: 01 February 2024

The aim of this paper is to establish the second main theorem for holomorphic curves from the annulus into a complex projective variety intersecting an arbitrary family of hypersurfaces. This is done by using the notion of "Distributive Constant" for a family of hypersurfaces with respect to a complex projective variety developed by Quang. We also give an explicit estimate for the level of truncation.
- Nevanlinna theory,
- second main theorem,
- holomorphic curves,
- hypersurfaces
Citation: Liu Yang, Yuehuan Zhu. Second main theorem for holomorphic curves on annuli with arbitrary families of hypersurfaces[J]. Electronic Research Archive, 2024, 32(2): 1365-1379. doi: 10.3934/era.2024063

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Abstract

The aim of this paper is to establish the second main theorem for holomorphic curves from the annulus into a complex projective variety intersecting an arbitrary family of hypersurfaces. This is done by using the notion of "Distributive Constant" for a family of hypersurfaces with respect to a complex projective variety developed by Quang. We also give an explicit estimate for the level of truncation.

References

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