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pro vyhledávání: '"Huynh, Dinh Tuan"'
We study the Waldschmidt constant of some configurations in the projective plane. In the first part, we show that the Waldschmidt constant of a set $\mathbb{X}$ of $n$ points where at least $n-3$ points among them lie on a line is either equal to $1,
Externí odkaz:
http://arxiv.org/abs/2410.05029
Autor:
Huynh, Dinh Tuan
In the first part of this paper, we establish some results around generalized Borel's Theorem. As an application, in the second part, we construct example of smooth surface of degree $d\geq 19$ in $\mathbb{CP}^3$ whose complements is hyperbolically e
Externí odkaz:
http://arxiv.org/abs/2407.16163
Autor:
Huynh, Dinh Tuan
We prove that if $f\colon\mathbb{C}^p\rightarrow\mathbb{P}^n(\mathbb{C})$ is a holomorphic mapping of maximal rank whose image lies in the Fermat hypersurface of degree $d>(n+1)\max\{n-p,1\}$, then its image is contained in a linear subspace of dimen
Externí odkaz:
http://arxiv.org/abs/2405.14907
Autor:
Huynh, Dinh Tuan
Let $\mathbf{K}$ be an algebraically closed field of arbitrary characteristic, complete with respect to a non-archimedean absolute value $|\,|$. We establish a Second Main Theorem type estimate for analytic map $f\colon \mathbf{K}\rightarrow\mathbb{P
Externí odkaz:
http://arxiv.org/abs/2405.14197
Autor:
Huynh, Dinh Tuan
Publikováno v:
Pacific J. Math. 330 (2024) 157-170
We prove that the Gauss map of a non-flat complete minimal surface immersed in $\mathbb{R}^n$ can omit a generic hypersurface $D$ of degree at most $ n^{n+2}(n+1)^{n+2}$.
Comment: 13 pages, comments are welcome. arXiv admin note: text overlap wi
Comment: 13 pages, comments are welcome. arXiv admin note: text overlap wi
Externí odkaz:
http://arxiv.org/abs/2401.07195
Let $\{D_i\}_{i=1}^{n+1}$ be $n+1$ hypersurfaces in $\mathbb{P}^n(\mathbb{C})$ with total degrees $\sum_{i=1}^{n+1}\text{deg}D_i\geqslant n+2$, satisfying one precise geometric (generic) condition. Then, for every algebraically nondegenerate entire h
Externí odkaz:
http://arxiv.org/abs/2310.05433
Autor:
Huynh, Dinh Tuan
Let $1\leq p\leq n$ be two positive integers. For a linearly nondegenerate holomorphic mapping $f\colon\mathbb{C}^p\rightarrow\mathbb{P}^n(\mathbb{C})$ of maximal rank intersecting a family of hyperplanes in general position, we obtain a Cartan's typ
Externí odkaz:
http://arxiv.org/abs/2306.14743
Publikováno v:
J Geom Anal 33, 308 (2023)
We construct explicit universal entire curves in projective spaces whose Nevanlinna characteristic functions grow slower than any preassigned transcendental growth rate. Moreover, we can make such curves to be hypercyclic for translation operations a
Externí odkaz:
http://arxiv.org/abs/2304.04929
Autor:
Huynh, Dinh Tuan, Xie, Song-Yan
We answer a basic question in Nevanlinna theory that Ahlfors currents associated to the same entire curve may be nonunique. Indeed, we will construct one exotic entire curve $f: \mathbb{C}\rightarrow X$ which produces infinitely many cohomologically
Externí odkaz:
http://arxiv.org/abs/2101.11973
By implementing jet differential techniques in non-archimedean geometry, we obtain a big Picard type extension theorem, which generalizes a previous result of Cherry and Ru. As applications, we establish two hyperbolicity-related results. Firstly, we
Externí odkaz:
http://arxiv.org/abs/2012.12656