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We prove a truncated second main theorem in the projective plane for entire curves which cluster on an algebraic curve.

Complex Variables · Mathematics 2016-10-24 Julien Duval , Dinh Tuan Huynh

In this paper, we establish a second main theorem for holomorphic maps with finite growth index on complex discs intersecting arbitrary families of hypersurfaces (fixed and moving) in projective varieties, which gives an above bound of the…

Complex Variables · Mathematics 2025-02-26 Si Duc Quang

Since the great work on holomorphic curves into algebraic varieties intersecting hypersurfaces in general position established by Ru in 2009, recently there has been some developments on the second main theorem into algebraic varieties…

Complex Variables · Mathematics 2021-09-07 Libing Xie , Tingbin Cao

In [Ann. of Math. 169 (2009)], Min Ru proved a second main theorem for algebraically nondegenerate holomorphic curves in complex projective varieties intersecting fixed hypersurface targets. In this paper, by introducing a new proof method…

Complex Variables · Mathematics 2018-11-13 Gerd Dethloff , Tran Van Tan

The tropical Nevanlinna theory is Nevanlinna theory for tropical functions or maps over the max-plux semiring by using the approach of complex analysis. The main purpose of this paper is to study the second main theorem with tropical…

Complex Variables · Mathematics 2026-01-29 Tingbin Cao , Jianhua Zheng

We establish a second main theorem for algebraic tori with slow growth moving targets with truncation to level 1. As the first application of this result, we prove the Green-Griffith-Lang conjecture for projective spaces with $n+1$…

Complex Variables · Mathematics 2021-03-31 Ji Guo , Chia-Liang Sun , Julie Tzu-Yueh Wang

In this note, we establish the following Second Main Theorem type estimate for every entire non-algebraically degenerate holomorphic curve $f\colon\mathbb{C}\rightarrow\mathbb{P}^n(\mathbb{C})$, in present of a {\sl generic} hypersuface…

Algebraic Geometry · Mathematics 2017-11-28 Dinh Tuan Huynh , Duc-Viet Vu , Song-Yan Xie

This paper has twofold. The first is to establish a second main theorem for meromorphic functions on the complex disc $\Delta (R_0)\subset\mathbb C$ with finite growth index and small functions, where the counting functions are truncated to…

Complex Variables · Mathematics 2024-03-26 Si Duc Quang

In this paper, we establish a truncated non-integrated defect relation for meromorphic mappings from a complete K\"ahler manifold into a projective variety intersecting a family of hypersurfaces located in subgeneral position, where the…

Complex Variables · Mathematics 2020-10-08 Si Duc Quang , Le Ngoc Quynh , Nguyen Thi Nhung

We apply an idea of Levin to obtain a non-truncated second main theorem for non-Archimedean analytic maps approximating algebraic hypersurfaces in subgeneral position. In some cases, for example when all the hypersurfaces are non-linear and…

Algebraic Geometry · Mathematics 2024-10-31 Ta Thi Hoai An , William Cherry , Nguyen Viet Phuong

A new proof of the Second Main Theorem with truncation level 1 for Zariski-dense holomorphic curves into Abelian varieties, which has just been proved by Yamanoi [Y2], is presented. Our proof is based on the idea of the "Radon transform"…

Complex Variables · Mathematics 2007-05-23 Ryoichi Kobayashi

In this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of C^m into P^n with truncated multiplicities and "few" targets. We also give a theorem of linear degeneration for such maps…

Complex Variables · Mathematics 2014-12-01 Gerd Dethloff , Tran Van Tan

In this paper, an Askey-Wilson version of the Wronskian-Casorati determinant $\mathcal{W}(f_{0}, \dots, f_{n})(x)$ for meromorphic functions $f_{0}, \dots, f_{n}$ is introduced to establish an Askey-Wilson version of the general form of the…

Complex Variables · Mathematics 2024-12-12 Chengliang Tan , Risto Korhonen

In this paper, we firstly give the definition of meromorphic function element and algebroid mapping. We also construct the algebroid function family in which the arithmetic, differential operations is closed. On basis of these works, we…

Complex Variables · Mathematics 2009-12-15 Daochun Sun , Zongsheng Gao , Huifang Liu

In this article, we prove that there are at most two meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)\ (n\geqslant 2)$ sharing $2n+2$ hyperplanes in general position regardless of multiplicity, where all zeros with…

Complex Variables · Mathematics 2019-02-27 Si Duc Quang

The purpose of this paper has twofold. The first is to establish a second main theorem for meromorphic functions on annuli and meromorphic function targets (may not be small functions) with truncated counting functions (truncation level 1)…

Complex Variables · Mathematics 2023-06-27 Si Duc Quang

We establish the second main theorem with the best truncation level one for an entire holomorphic curve $f:\C \to A$ into a semi-abelian variety $A$ and an arbitrary effective reduced divisor $D$ on $A$; the low truncation level is…

Complex Variables · Mathematics 2007-05-23 Junjiro Noguchi , Jörg Winkelmann , Katsutoshi Yamanoi

In this paper, we extend the uniqueness theorem for meromorphic mappings to the case where the family of hyperplanes depends on the meromorphic mapping and where the meromorphic mappings may be degenerate.

Complex Variables · Mathematics 2014-12-01 G. Dethloff , Tan Tran Van , Si Duc Quang

Let $f$ be an algebraically nondegenerate meromorphic mapping from $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ and let $Q_1,...,Q_q$ be $q$ hypersurfaces in $\mathbb P^n(\mathbb C)$ of degree $d_i$, in $N-$subgeneral position. In this…

Complex Variables · Mathematics 2018-08-30 Si Duc Quang

We study the Second Main Theorem in non-archimedean Nevanlinna theory, giving an improvement to the non-archimedean Second Main Theorems of Ru and An in the case where all the hypersurfaces have degree greater than one and all intersections…

Complex Variables · Mathematics 2013-03-19 Aaron Levin