Journal of Symplectic Geometry

Volume 17 (2019)

Number 6

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

Pages: 1793 – 1833



Melinda Lanius (Department of Mathematics, University of Arizona, Tucson, Az., U.S.A.)


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.

Received 29 May 2017

Accepted 27 August 2018

Published 17 January 2020