A characterization of diagonal Poisson structures

Published 12 Dec 2013 in math.SG and math.AG | (1312.3596v2)

Abstract: The degeneracy locus of a generically symplectic Poisson structure on a Fano manifold is always a singular hypersurface. We prove that there exists just one family of generically symplectic Poisson structures in Fano manifold with cyclic Picard group having a reduced simple normal crossing degeneracy locus.

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