Commun. Math. Res., 35 (2019), pp. 97-105.
Published online: 2019-12
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Let ${\cal F}$ be a family of holomorphic curves of a domain $D$ in ${\bf C}$ into a closed subset $X$ in ${\mathbb P}^N(\bf C)$. Let $Q_1(z),\,\cdots,\,Q_{2t+1}(z)$ be moving hypersurfaces in ${\mathbb P}^N(\bf C)$ located in pointwise $t$-subgeneral position with respect to $X$. If each pair of curves $f$ and $g$ in ${\cal F}$ share the set $\{Q_1(z),\,\cdots,\,Q_{2t+1}(z)\}$, then ${\cal F}$ is normal on $D$. This result greatly extend some earlier theorems related to Montel's criterion.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2019.02.01}, url = {http://global-sci.org/intro/article_detail/cmr/13480.html} }Let ${\cal F}$ be a family of holomorphic curves of a domain $D$ in ${\bf C}$ into a closed subset $X$ in ${\mathbb P}^N(\bf C)$. Let $Q_1(z),\,\cdots,\,Q_{2t+1}(z)$ be moving hypersurfaces in ${\mathbb P}^N(\bf C)$ located in pointwise $t$-subgeneral position with respect to $X$. If each pair of curves $f$ and $g$ in ${\cal F}$ share the set $\{Q_1(z),\,\cdots,\,Q_{2t+1}(z)\}$, then ${\cal F}$ is normal on $D$. This result greatly extend some earlier theorems related to Montel's criterion.