A classification of star log symplectic structures on a compact oriented\n surface

2017/05/04 by Melinda Lanius, Lanius, Melinda
Mathematics · #53D05 #53D17 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1705.01793

openalex publication_date 2017/05/04 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Given a compact oriented surface, we classify log Poisson bi-vectors whose\ndegeneracy loci are locally modeled by a finite set of lines in the plane\nintersecting at a point. Further, we compute the Poisson cohomology of such\nstructures and discuss the relationship between our classification and the\nsecond Poisson cohomology.\n

Related

• Log Floer cohomology for oriented log symplectic surfaces
• Poisson cohomology of a class of log symplectic manifolds
• A local Torelli theorem for log symplectic manifolds
• A classification of topologically stable Poisson structures on a compact oriented surface
• Holomorphic curves in log-symplectic manifolds