关于奇异复数空间上带有 L2 估计数的∂--方程

Pub Date : 2024-04-22 DOI:10.1093/imrn/rnae076

Zhenqian Li, Zhi Li, Xiangyu Zhou

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引用次数: 0

摘要

在本文中，我们提出了带有加权$L^{2}$估计的$overline \partial $-方程的不可解性，其中涉及一般奇异正复空间上的曲率项。此外，在非正态情况下，我们还完整地描述了带加权 $L^{2}$ 估计的 $overline \partial $-方程对平面曲线奇点及其高维变体的 $L^{2}$ 可解性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the ∂—-Equation with L2 Estimates on Singular Complex Spaces

In this paper, we present the unsolvability of $\overline \partial $-equation with weighted $L^{2}$ estimates involved curvature terms on any singular normal complex space in general. Moreover, in the non-normal case, we also give a complete description on $L^{2}$-solvability of the $\overline \partial $-equation with weighted $L^{2}$ estimates for plane curve singularities and their variants in the higher dimension.

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