{"paper":{"title":"Kahler geometry of toric manifolds in symplectic coordinates","license":"","headline":"","cross_cats":["math.AG","math.SG"],"primary_cat":"math.DG","authors_text":"Miguel Abreu","submitted_at":"2000-04-19T09:15:46Z","abstract_excerpt":"A theorem of Delzant states that any symplectic manifold $(M,\\om)$ of dimension $2n$, equipped with an effective Hamiltonian action of the standard $n$-torus $\\T^n = \\R^{n}/2\\pi\\Z^n$, is a smooth projective toric variety completely determined (as a Hamiltonian $\\T^n$-space) by the image of the moment map $\\phi:M\\to\\R^n$, a convex polytope $P=\\phi(M)\\subset\\R^n$. In this paper we show, using symplectic (action-angle) coordinates on $P\\times \\T^n$, how all $\\om$-compatible toric complex structures on $M$ can be effectively parametrized by smooth functions on $P$. We also discuss some topics suit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0004122","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0004122/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}