Semiglobal results for d-bar on complex spaces with arbitrary singularities, Part II

TL;DR

This paper establishes L2 solvability results for the d-bar operator on complex spaces with arbitrary singularities, providing new tools for solving d-bar equations in singular settings and offering an alternative proof for existing theorems.

Contribution

It introduces weighted L2-solvability results for d-bar on forms vanishing at high order on singular sets, extending previous work to more general singular complex spaces.

Findings

L2 results for d-bar on forms with high order vanishing

Weighted L2-solvability for compactly supported d-bar closed forms

Alternative proof of Merker and Porten's theorem

Abstract

We obtain some L2 results for d-bar on forms that vanish to high order on the singular set of a complex space. As a consequence of our main theorem we obtain weighted L2-solvability results for compactly supported d-bar closed (p,q) forms defined on certain relatively compact subdomains of the complex space. The latter result can be used to give an alternate proof of a theorem of Merker and Porten.