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• W2087907966 abstract "In this paper, we study the interplay between modules and sub-objects in holomorphic Poisson geometry. In particular, we define a new notion of ‘residue’ for a Poisson module, analogous to the Poincaré residue of a meromorphic volume form. We then explore the interaction between the residues of the canonical line bundle of a Poisson manifold and its degeneracy loci, where the rank of the Poisson structure drops. As an application, we provide new evidence in favor of Bondal's conjecture that the rank at most 2k locus of a Fano Poisson manifold always has dimension at least 2k + 1. In particular, we show that the conjecture holds for Fano 4-folds. We also apply our techniques to a family of Poisson structures defined by Feĭgin and Odesskiĭ, where the degeneracy loci are given by the secant varieties of elliptic normal curves." @default.
• W2087907966 created "2016-06-24" @default.
• W2087907966 creator A5050336301 @default.
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• W2087907966 date "2013-02-18" @default.
• W2087907966 modified "2023-10-04" @default.
• W2087907966 title "Poisson modules and degeneracy loci" @default.
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• W2087907966 doi "https://doi.org/10.1112/plms/pds090" @default.
• W2087907966 hasPublicationYear "2013" @default.
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