Duality between Bott-Chern and Aeppli Cohomology on Non-Compact Complex Manifolds

Abstract

In this paper we establish duality theorems relating Bott-Chern and Aeppli cohomology, both with and without compact support, on non-compact complex manifolds under suitable pseudoconvexity assumptions. In particular, on Stein manifolds we obtain a full Bott-Chern-Aeppli duality extending Serre duality for Dolbeault cohomology. We also show that these results fail in general without pseudoconvexity assumptions by constructing explicit counterexamples on non-compact complex surfaces.