A version of Cartan–Nochka's theorem for non-Archimedean holomorphic curves with integrated reduced counting functions
UDC 517.5 Let $\mathbb{K}$ be an algebraically closed field of characteristic $0,$ completed with respect to a non-Archimedean absolute value and let $\mathbb{P}^n(\mathbb{K})$ be an $n$-dimensional projective space over $\mathbb{K}.$ A collection $\mathcal H = \{H_1,\ldots,H_q\} \in \mathbb{P}^n(\m...
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| Datum: | 2026 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8755 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.5
Let $\mathbb{K}$ be an algebraically closed field of characteristic $0,$ completed with respect to a non-Archimedean absolute value and let $\mathbb{P}^n(\mathbb{K})$ be an $n$-dimensional projective space over $\mathbb{K}.$ A collection $\mathcal H = \{H_1,\ldots,H_q\} \in \mathbb{P}^n(\mathbb{K}),$ $q \geq N+1,$ is said to be in $N$-subgeneral position if, for any $1\leq i_1<\ldots<i_{N+1}\leq q,$ we have $\bigcap_{j=1}^{N+1} H_{i_j} = \varnothing.$ We prove a version of the second main theorem for non-Archimedean holomorphic curves intersecting hyperplanes in $N$-subgeneral position with integrated reduced counting functions. |
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| DOI: | 10.3842/umzh.v77i9.8755 |