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arXiv 2602.033322026-02math.CV

$L^2$-Dolbeault 解析与弱伪凸复空间上 Nadel 消失定理

$L^2$-Dolbeault resolutions and Nadel vanishing on weakly pseudoconvex complex spaces with singular Hermitian metrics

Chuo University（中央大学）

Yuta Watanabe

备注：: v2: 22 pages. Mainly revised the introduction and Section 4 in light of prior work, and removed the former Section 4. v1: 24 pages

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AI总结：

本文研究了弱伪凸复空间上 $L^2$-Dolbeault 解析与 $L^2$-估计，推广了 Nadel 消失定理。

摘要：

本文旨在发展更一般的 $L^2$-理论用于复空间上的 $\overline{\partial}$-算子，我们提供了 $L^2$-Dolbeault 细解析和同构以及 $L^2$-估计，用于具有奇点 Hermitian度量的复空间上的全纯线丛。作为应用，我们获得了 Nadel 消失定理的几个推广。

英文摘要：

In this paper, in order to develop a more general $L^2$-theory for the $\overline{\partial}$-operator on complex spaces, we provide $L^2$-Dolbeault fine resolutions and isomorphisms, and $L^2$-estimates, for holomorphic line bundles on complex spaces equipped with singular Hermitian metrics. As applications, we obtain several generalizations of the Nadel vanishing theorem.

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