Holomorphic Curves into ${\mathbb P}^N({\bf C})$ That Share a Set of Moving Hypersurfaces (Communications in Mathematical Research, 2019)
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 $Q_1(z),\,…,\,Q_{2t+1}(z)$ 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 $\{Q_1(z),\,…,\,Q_{2t+1}(z)\}$, then ${\cal F}$ is normal on $D$. This result greatly extend some earlier theorems related to Montel's criterion.
Keywords: Holomorphic mapping; normal family; value distribution theory; complex projective space; hypersuface