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

## TL;DR

This paper classifies a specific type of log Poisson structures on compact surfaces, computes their Poisson cohomology, and explores their mathematical properties and relationships.

## Contribution

It provides a comprehensive classification of star log symplectic structures on compact oriented surfaces and analyzes their Poisson cohomology.

## Key findings

- Classification of log Poisson bi-vectors with line degeneracy loci
- Calculation of Poisson cohomology for these structures
- Discussion of the relationship with second Poisson cohomology

## Abstract

Given a compact oriented surface, we classify log Poisson bi-vectors whose degeneracy loci are locally modeled by a finite set of lines in the plane intersecting at a point. Further, we compute the Poisson cohomology of such structures and discuss the relationship between our classification and the second Poisson cohomology.