A characterization of diagonal Poisson structures
classification
🧮 math.SG
math.AG
keywords
poissondegeneracyfanogenericallylocusmanifoldstructuressymplectic
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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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