In this paper, we present the unsolvability of ∂-equation with weighted L² 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 L²-solvability of the ∂-equation with weighted L² estimates for plane curve singularities and their variants in the higher dimension.
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Li et al. (2024) studied this question.
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