Non-exactness of toric Poisson structures

Published 25 Apr 2022 in math.DG | (2204.11916v1)

Abstract: We prove that a Poisson structure on a projective toric variety which is invariant by the torus action and whose symplectic leaves are the torus orbits is not exact. This is deduced from a geometric criterion for non-exactness of Poisson structures with a finite number of symplectic leaves.

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