Related papers: An explicit estimate on multiplicity truncation in…
In this paper, we establish a second main theorem for holomorphic curve intersecting hypersurfaces in general position in projective space with level of truncation. As an application, we reduce the number hypersurfaces in uniqueness problem…
The purpose of this paper has twofold. The first is to establish a second main theorem with truncated counting functions for algebraically nondegenerate meromorphic mappings into an arbitrary projective variety intersecting a family of…
We establish second main theorems for holomorphic curves into a projective subvary $V \subset \mathbb{P}^n(\mathbb{C})$ of dimension $k$, intersecting hypersurfaces in $N$-subgeneral position with respect to $V$ $(N > k)$. Our results…
By using Brownian motion and stochastic calculus, we establish a second main theorem for holomorphic curves into a projective subvariety $V\subset\mathbb P^n(\mathbb C)$ with an arbitrary family $\mathcal Q$ of $q$ hypersurfaces…
The purpose of this article is twofold. The first is to prove a second main theorem for meromorphic mappings of $\C^m$ into a complex projective variety intersecting hypersurfaces in subgeneral position with truncated counting functions.…
The possibility of reversion of the inequality in the Second Main Theorem of Cartan in the theory of holomorphic curves in projective space is discussed. A new version of this theorem is proved that becomes an asymptotic equality for a…
In this article, we show some new second main theorems for the mappings and moving hyperplanes of $\P^n(\C)$ with truncated counting functions. Our results are improvements of recent previous second main theorems for moving hyperplanes with…
In this paper, we prove some fundamental theorems for holomorphic curves on angular domain intersecting a hypersurface, finite set of fixed hyperplanes in general position and finite set of fixed hypersurfaces in general position on complex…
The purpose of this article is to show a second main theorem with the explicit truncation level for holomorphic mappings of $ \mathbb{C} $ (or of a compact Riemann surface) into a compact complex manifold sharing divisors in subgeneral…
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"…
We prove a truncated second main theorem in the projective plane for entire curves which cluster on an algebraic curve.
In 1983, Nochka proved a conjecture of Cartan on defects of holomorphic curves in CP^n relative to a possibly degenerate set of hyperplanes. In this paper, we generalize the Nochka's theorem to the case of curves in a complex projective…
In this article, we establish some new second main theorems for meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ and moving hypersurfaces with truncated counting functions. A uniqueness theorem for these mappings sharing…
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…
We extend the difference analogue of Cartan's second main theorem for the case of slowly moving periodic hyperplanes, and introduce two different natural ways to find a difference analogue of the truncated second main theorem. As…
In this paper, we give some extension of fundamental theorems in Nevanlinna - Cartan theory for holomorphic curve on M punctured complex planes. As an application, we establish a result for uniqueness problem of holomorphic curve by inverse…
In 1979, B. Shiffman conjectured that if f is an algebraically nondegenerate holomorphic map of C into P^n and D_1,...,D_q are hypersurfaces in P^n in general position, then the sum of the defects is at most n+1. This conjecture was proved…
In this article, we establish some new second main theorems for meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ and moving hyperplanes with truncated counting functions. Our results are improvements of the previous…
The purpose of this article has two fold. The first is to generalize some recent second main theorems for the mappings and moving hyperplanes of $\P^n(\C)$ to the case where the counting functions are truncated multiplicity (by level $n$)…
Let $\mathbb F$ be an algebraically closed field of characteristic $p\ge 0$, which is complete with respect to a non-Archimedean absolute value. Let $V$ be a projective subvariety of $\mathbb P^M(\mathbb F)$. In this paper, we will prove…