Meromorphic mappings into projective varieties intersecting arbitrary families of moving hypersurfaces
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911716715003904 |
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| author | Quang, Si Duc Chi, Nguyen Linh |
| author_facet | Quang, Si Duc Chi, Nguyen Linh |
| contents | 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 $Δ_{\mathcal Q,V}(3\dim V-1)$, which is independent of the mapping $f$, where $Δ_{\mathcal Q,V}$ denotes the distributive constant of $\mathcal Q$ with respect to $V$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26034 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Meromorphic mappings into projective varieties intersecting arbitrary families of moving hypersurfaces Quang, Si Duc Chi, Nguyen Linh Complex Variables 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 $Δ_{\mathcal Q,V}(3\dim V-1)$, which is independent of the mapping $f$, where $Δ_{\mathcal Q,V}$ denotes the distributive constant of $\mathcal Q$ with respect to $V$. |
| title | Meromorphic mappings into projective varieties intersecting arbitrary families of moving hypersurfaces |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2605.26034 |