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

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.

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Received 29 May 2017

Accepted 27 August 2018

Published 17 January 2020