On cohomological obstructions to the existence of log symplectic structures

2013/03/25 by Ioan Mărcuț, Ioan Marcut, Marcut, Ioan +2
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.DG #math.SG

paper · pdf · doi:10.48550/arxiv.1303.6246

3 pages. To appear in JSG

openalex publication_date 2013/03/25 · arxiv created 2014/03/11 · arxiv updated 2014/03/12 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

We prove that a compact log symplectic manifold has a class in the second cohomology group whose powers, except maybe for the top, are nontrivial. This result gives cohomological obstructions for the existence of b-log symplectic structures similar to those in symplectic geometry.

Related

• Poisson cohomology of a class of log symplectic manifolds
• Mixed Hodge structures in log symplectic geometry
• Complex symplectic structures: deformations and cohomology
• Non-standard Symplectic Structures via Symplectic Cohomology
• A local Torelli theorem for log symplectic manifolds