Volume 35, Issue 2
Holomorphic Curves into ${\mathbb P}^N({\bf C})$ That Share a Set of Moving Hypersurfaces

Liu Yang

Commun. Math. Res., 35 (2019), pp. 97-105.

Published online: 2019-12

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  • Abstract

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.

  • Keywords

Holomorphic mapping, normal family, value distribution theory, complex projective space, hypersuface

  • AMS Subject Headings

32A19, 32H30, 30D45, 32H02

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yangliu20062006@126.com (Liu Yang)

  • BibTex
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  • TXT
@Article{CMR-35-97, author = {Yang , Liu}, title = {Holomorphic Curves into ${\mathbb P}^N({\bf C})$ That Share a Set of Moving Hypersurfaces}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {35}, number = {2}, pages = {97--105}, abstract = {

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} }
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.

Liu Yang. (2019). Holomorphic Curves into ${\mathbb P}^N({\bf C})$ That Share a Set of Moving Hypersurfaces. Communications in Mathematical Research . 35 (2). 97-105. doi:10.13447/j.1674-5647.2019.02.01
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