论文标题
在紧凑的kähler歧管上的kähler电流的扩展
On the extensions of Kähler currents on compact Kähler manifolds
论文作者
论文摘要
令$（x，ω）$是一个紧凑的kähler歧管，带有kähler形式的复杂尺寸$ n $的$ω$，而$ v \ subset x $是一个紧凑的正数$ k <n $的紧凑型复杂submanifold。假设$ v $可以将$ x $嵌入为holomorphic vector捆绑包的零部分，也可以超过$ v $等级$ n-k $。令$φ$为$ v $上的$ω| _v $ -psh函数。在本文中，我们证明$ x $上有一个严格的$ω$ -PSH函数$φ$，因此$φ| _v =φ$。该结果对Collins-Tosatti和Dinew-Guedj-Zeriahi提出的开放问题为部分答案提供了部分答案。我们还讨论了大型班级中Kähler电流的可能扩展。
Let $(X,ω)$ be a compact Kähler manifold with a Kähler form $ω$ of complex dimension $n$, and $V\subset X$ is a compact complex submanifold of positive dimension $k<n$. Suppose that $V$ can be embedded in $X$ as a zero section of a holomorphic vector bundle or rank $n-k$ over $V$. Let $φ$ be a strictly $ω|_V$-psh function on $V$. In this paper, we prove that there is a strictly $ω$-psh function $Φ$ on $X$, such that $Φ|_V=φ$. This result gives a partial answer to an open problem raised by Collins-Tosatti and Dinew-Guedj-Zeriahi, for the case of Kähler currents. We also discuss possible extensions of Kähler currents in a big class.
