论文标题
关于Quasiplurisubharmonic功能的扩展
On the extension of quasiplurisubharmonic functions
论文作者
论文摘要
令$（v，ω）$为紧凑的kähler歧管，以便$ v $允许Zariski-Open Stein套装的封面，并带有$ω$在封面的每个元素上具有严格的Plurisubharmonic详尽潜力。如果$ x \ subset v $是一种分析性亚变量，我们证明$ x $上的任何$ω| _x $ -plurisubharmonic函数都扩展到$ v $上的$ω$ -plurisubharmonic函数。 该结果概括了我们对富含线束的奇异指标扩展的先前结果。它允许一个人证明，真正的Neron-Severi Space中的任何超越Kähler类$ ns _ {\ Mathbb r}（v）$都具有此扩展属性。
Let $(V,ω)$ be a compact Kähler manifold such that $V$ admits a cover by Zariski-open Stein sets with the property that $ω$ has a strictly plurisubharmonic exhaustive potential on each element of the cover. If $X\subset V$ is an analytic subvariety, we prove that any $ω|_X$-plurisubharmonic function on $X$ extends to a $ω$-plurisubharmonic function on $V$. This result generalizes a previous result of ours on the extension of singular metrics of ample line bundles. It allows one to show that any transcendental Kähler class in the real Neron-Severi space $NS_{\mathbb R}(V)$ has this extension property.
