{"paper":{"title":"Poisson modules and degeneracy loci","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.SG"],"primary_cat":"math.AG","authors_text":"Brent Pym, Marco Gualtieri","submitted_at":"2012-03-20T00:11:28Z","abstract_excerpt":"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 Poincar\\'e residue of a meromorphic volume form. Of particular interest is 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 favour of Bondal's conjecture that the rank \\leq 2k locus of a Fano Poisson manifold always has dimension \\geq 2k+1. In parti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4293","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}