arXiv subjects

Nguyen Linh Chi

Publications and source records attributed to Nguyen Linh Chi.

2 recordsLinked to original sources

arXiv2026

Meromorphic mappings into projective varieties intersecting arbitrary families of moving hypersurfaces

In this paper, we establish a general second main theorem for meromorphic mappings from $\mathbb C^m$ into a subvariety $V$ of $\mathbb P^n(\mathbb C)$ with respect to an arbitrary family of slowly moving hypersurfaces $\mathcal Q=\{Q_1,\ldots,Q_q\}$. In contrast to the usual setting, the mapping is not required to be algebraically nondegenerate over the field $\mathcal K_{\mathcal Q}$. Moreover, the truncation levels of the counting functions are explicitly estimated, and the total defect bound is given by $\Delta_{\mathcal Q,V}(3\dim V-1)$, which is independent of the mapping $f$, where $\Delta_{\mathcal Q,V}$ denotes the distributive constant of $\mathcal Q$ with respect to $V$.

math.CV↗

arXiv2026

A Brownian-Motion Approach to the Second Main Theorem for Meromorphic Mappings and Hypersurfaces with Truncated Counting Functions

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 $Q_1,\ldots,Q_q$ concerning its distributive constant $\Delta_{\mathcal Q,V}$. In our result, the counting functions are truncated to level $H_V(d)-1$, where $d=lcd(\deg Q_1,\ldots,\deg Q_d)$ and $H_V(d)$ is the Hilbert function of $V$. As an application of the second main theorem, we give a uniqueness theorem for holomorphic curves from $\mathbb C$ into $V$ sharing an arbitrary family of hypersurfaces regardless of multiplicity.

math.CV↗