L²-Serre duality on singular complex spaces and rational singularities

2014/01/18 by Ruppenthal, Jean
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1401.4563

Abstract

In the present paper, we devise a version of topological L²-Serre duality for singular complex spaces with arbitrary singularities. This duality is used to deduce various new L²-vanishing theorems for the ∂-equation on singular spaces. It is shown that complex spaces with rational singularities behave quite tame with respect to the ∂-equation in the L²-sense. More precisely: a singular point is rational if and only if the L²-∂-complex is exact in this point. So, we obtain an L²-∂-resolution of the structure sheaf in rational singular points.

Related

• L²-Serre duality on singular complex spaces and applications
• L² Serre Duality on Domains in Complex Manifolds and Applications
• L²-theory for the ∂-operator on complex spaces with isolated singularities
• The ∂-equation, duality, and holomorphic forms on a reduced complex space
• Semiglobal results for ∂ on a complex space with arbitrary singularities