标题： 奇异度量的向量丛上的Segre形式和Lelong数 显示英文标题

标题： Segre forms of singular metrics on vector bundles and Lelong numbers

摘要： 设 $E\to X$ 是一个全纯向量丛，并且具有奇异的Griffiths负Hermitian度量 $h$，该度量具有解析奇点。 给定一个光滑参考度量 $h_0$，可以定义一个称为关联Segre形式的电流 $s(E,h,h_0)$，它定义了期望的Bott-Chern类，并且在光滑处与 $h$ 的通常Segre形式一致。 我们证明，若度量在非无界集外是光滑的，则 $s(E,h,h_0)$ 是一列光滑度量的Segre形式的极限；一般情况下，它是无界集为空的度量的Segre形式的极限。 还可以定义一个相关的陈形式$c(E,h,h_0)$，我们证明了如果奇点是整数型的，则$s(E,h,h_0)$和$c(E,h,h_0)$的勒让德数是整数，并且对于$s(E,h,h_0)$来说非负。我们还将这些结果推广到了具有解析奇点的一类稍大的奇异度量上。 显示英文摘要

摘要： Let $E\to X$ be a holomorphic vector bundle with a singular Griffiths negative Hermitian metric $h$ with analytic singularities. One can define, given a smooth reference metric $h_0$, a current $s(E,h,h_0)$ that is called the associated Segre form, which defines the expected Bott-Chern class and coincides with the usual Segre form of $h$ where it is smooth. We prove that $s(E,h,h_0)$ is the limit of the Segre forms of a sequence of smooth metrics if the metric is smooth outside the unbounded locus, and in general as a limit of Segre forms of metrics with empty unbounded locus. One can also define an associated Chern form $c(E,h,h_0)$ and we prove that the Lelong numbers of $s(E,h,h_0)$ and $c(E,h,h_0)$ are integers if the singularities are integral, and non-negative for $s(E,h,h_0)$. We also extend these results to a slightly larger class of singular metrics with analytic singularities.