Abstract: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 $V$.
| Comments: | 20 pages |
| Subjects: | Complex Variables (math.CV) |
| Cite as: | arXiv:2605.26034 [math.CV] |
| (or arXiv:2605.26034v1 [math.CV] for this version) | |
| https://doi.org/10.48550/arXiv.2605.26034 arXiv-issued DOI via DataCite (pending registration) |
From: Duc Quang Si [view email]
[v1]
Mon, 25 May 2026 17:01:53 UTC (16 KB)
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