论文标题
在$ l^2 $扩展定理上，来自对数典型措施的日志典型中心
On an $L^2$ extension theorem from log-canonical centres with log-canonical measures
论文作者
论文摘要
为了证明一个ohsawa-takegoshi类型$ l^2 $扩展定理，并具有$ l^2 $的估计值相对于日志典型（LC）措施，这是一系列措施，每个措施均支持通过乘数和lc通过倍增器定义的特定编码中心的LC中心，以提供$ l^2 $的估计，以提供$ l^2 $ 2 $^2 $^2 $^2 $ $ x $。引入了环境空间$ x $的$ l^2 $规范的全体形态家族，该家族在LC估计的情况下显示为$ l^2 $ normal“将霍姆形成型”。此外，在某个标准式下，后一种规范被证明是不变的，这会导致“非宇宙” $ l^2 $估算在紧凑型$ x $上。提供了$ \ Mathbb {P}^3 $的明确示例，并提供了详细的计算，以验证来自各种编码的LC中心扩展的预期$ L^2 $估计值，并为一般估计值提供了提示。
With a view to prove an Ohsawa-Takegoshi type $L^2$ extension theorem with $L^2$ estimates given with respect to the log-canonical (lc) measures, a sequence of measures each supported on lc centres of specific codimension defined via multiplier ideal sheaves, this article is aiming at providing evidence and possible means to prove the $L^2$ estimates on compact Kähler manifolds $X$. A holomorphic family of $L^2$ norms on the ambient space $X$ is introduced which is shown to "deform holomorphically" to an $L^2$ norm with respect to an lc-measure. Moreover, the latter norm is shown to be invariant under a certain normalisation which leads to a "non-universal" $L^2$ estimate on compact $X$. Explicit examples on $\mathbb{P}^3$ with detailed computation are presented to verify the expected $L^2$ estimates for extensions from lc centres of various codimensions and to provide hint for the proof of the estimates in general.
