TY - JOUR T1 - Holomorphic Curves into ${\mathbb P}^N({\bf C})$ That Share a Set of Moving Hypersurfaces AU - Yang , Liu JO - Communications in Mathematical Research VL - 2 SP - 97 EP - 105 PY - 2019 DA - 2019/12 SN - 35 DO - http://doi.org/10.13447/j.1674-5647.2019.02.01 UR - https://global-sci.org/intro/article_detail/cmr/13480.html KW - Holomorphic mapping, normal family, value distribution theory, complex projective space, hypersuface AB -

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.