Geometry and Topology Seminar: Non-Kahler symplectic forms on complex surfaces

Abstract: Since Thurston’s first example of a non-Kahler symplectic 4-manifold, people have gradually realized that the world of Kahler manifolds only occupies a tiny part of the symplectic world. However, when restricted to a complex surface with even first Betti number, determining whether it has a non-Kahler symplectic form is more subtle. A mega result is that any such complex surface always admits Kahler structures. In this talk, we review what is known about this question and present some progress in the case of Kodaira dimension zero. This talk is based on the preprint arXiv:2407.10217.

Host: Xiang Tang