The ∂-equation, duality, and holomorphic forms on a reduced complex space

2015/06/25 by Kalm, Håkan Samuelsson
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1506.07842

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 precise condition for the ∂-equation to be globally solvable. Our results extend results for (0,q)-forms and give information about holomorphic p-forms on singular spaces.

Related

• The ∂-equation for (p,q)-forms on a non-reduced analytic space
• L² Serre Duality on Domains in Complex Manifolds and Applications
• Solving the ∂ ∂ with prescribed support
• The ∂ ∂-problem for a differential forms with boundary value in currents sense defined in a contractible completely strictly pseudoconvex domain of a complex manifold
• L²-Serre duality on singular complex spaces and rational singularities