A Dolbeault-Grothendieck lemma on complex spaces via Koppelman formulas

Abstract

Let $X$ be a complex space of pure dimension. We introduce fine sheaves $\A^X_q$ of $(0,q)$-currents, which coincides with the sheaves of smooth forms on the regular part of $X$, so that the associated Dolbeault complex yields a resolution of the structure sheaf $\hol^X$. Our construction is based on intrinsic and quite explicit semi-global Koppelman formulas.

References in corpus (6)

• Pure Hodge structure on the $L_2$-cohomology of varieties with isolated singularities
• Various approaches to products of residue currents
• Analytic continuation of residue currents
• Koppelman formulas and the $\dbar$-equation on an analytic space
• Global effective versions of the Brian\ccon-Skoda-Huneke theorem
• Residual d-bar-cohomology and the complex Radon transform on subvarieties of CPn

Cited by in corpus (1)

• Global effective versions of the Brian\ccon-Skoda-Huneke theorem