Second main theorem for Holomorphic curves intersecting a Fermat-type hypersurface in projective spacel

Let $s, b, d$ be positive integers with $(s+bd)-(n+1)(s+bn)>0$. Let $R_{i}$ be homogeneous polynomials of degree $s$ and $Q_i$ be homogeneous polynomials of degree $b$. For an algebraically non-degenerate holomorphic curve $f\colon\mathbb{C}\rightarrow\mathbb{C} \mathbb{P}^n$, for a Fermat-type hypersurface of the form $\sum_{i=0}^{n} Q_i R_{i}^{d}=0$, we obtain a Second Main Theorem type estimate in which the counting function are truncated to level $n$.

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Journal
HUE UNIVERSITY JOURNAL OF SCIENCE NATURAL SCIENCE
Published
2025-06-16
DOI
https://doi.org/10.26459/hueunijns.v134i1b.7551
Primary Topic
Meromorphic and Entire Functions
Type
article
Field-Weighted Citation Impact
0.00

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article

Second main theorem for Holomorphic curves intersecting a Fermat-type hypersurface in projective spacel

Nguyễn Duy Cường, Nhat Minh Tran, H. Nguyen, The Hieu Pham
HUE UNIVERSITY JOURNAL OF SCIENCE NATURAL SCIENCE
Meromorphic and Entire Functions
article

Second main theorem for Holomorphic curves intersecting a Fermat-type hypersurface in projective spacel

Nguyễn Duy Cường, Nhat Minh Tran, H. Nguyen, The Hieu Pham
article en

Abstract

Let $s, b, d$ be positive integers with $(s+bd)-(n+1)(s+bn)>0$. Let $R_{i}$ be homogeneous polynomials of degree $s$ and $Q_i$ be homogeneous polynomials of degree $b$. For an algebraically non-degenerate holomorphic curve $f\colon\mathbb{C}\rightarrow\mathbb{C} \mathbb{P}^n$, for a Fermat-type hypersurface of the form $\sum_{i=0}^{n} Q_i R_{i}^{d}=0$, we obtain a Second Main Theorem type estimate in which the counting function are truncated to level $n$.

HUE UNIVERSITY JOURNAL OF SCIENCE NATURAL SCIENCEVol. 134(1B)
Hue University of Education (VN)
Đại học Huế
Openalex Percentile: Top 80%
Meromorphic and Entire Functions
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