Related papers: The Second Main Theorem for Holomorphic Curves int…
Let f:C -> A be an entire holomorphic curve into a semi-Abelian variety A. Then the Zariski closure of f(C) is a translate of a semi-Abelian subvariety of A (logarithmic Bloch-Ochiai's theorem). The purpose of the present paper is to…
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"…
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…
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…
We prove a truncated second main theorem in the projective plane for entire curves which cluster on an algebraic curve.
The algebraic degeneracy of holomorphic curves in a semi-Abelian variety omitting a divisor is proved (Lang's conjecture generalized to semi-Abelian varieties) by making use of the {\it jet-projection method} and the logarithmic Wronskian…
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…
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…
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…
We prove a product decomposition of the Zariski closure of the jet lifts of a holomorphic map f from C into a semi-abelian variety A, provided that f is of finite order. On the other hand, by giving an example of such a map f into a three…
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…
In this paper, we prove a lemma on logarithmic derivative for holomorphic curves from annuli into K\"{a}hler compact manifold and. As its application, a second main theorem for holomophic curves from annuli into semi abelian varieties…
Yan and Chen proved a weak Cartan-type second main theorem for holomorphic curves meeting hypersurfaces in projective space that included truncated counting functions. Here we give an explicit estimate for the level of truncation.
Applying the Second Main Theorem we deal with the algebraic degeneracy of entire holomorphic curves from the complex plane into a complex algebraic normal variety of positive log Kodaira dimension that admits a finite proper morphism to a…
Recently, there are many developments on the second main theorem for holomorphic curves into algebraic varieties intersecting divisors in general position or subgeneral position. In this paper, we refine the concept of subgeneral position…
We establish a Second Main Theorem for entire holomorphic curves \( f: \mathbb{C} \to \mathbb{P}^2 \) intersecting a generic configuration of three conics \(\mathcal{C}= \mathcal{C}_1+ \mathcal{C}_2+ \mathcal{C}_3 \) in the complex…
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…
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…
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…