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

Abstract

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.