The $${\bar{\partial }}$$-Equation, Duality, and Holomorphic Forms on a Reduced Complex Space

Abstract

We solve the∂-equation for (p, q)-forms locally on any reduced pure-dimensional complex space and we prove an explicit version of Serre duality by introducing suitable concrete fine sheaves of certain (p, q)-currents. In particular this gives a condition for the∂-equation to be globally solvable. Our results also give information about holomorphic p-forms on singular spaces.