{"paper":{"title":"Complex symplectomorphisms and pseudo-K\\\"ahler islands in the quantization of toric manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jo\\~ao P. Nunes, Jos\\'e M. Mour\\~ao, William D. Kirwin","submitted_at":"2014-11-11T13:09:17Z","abstract_excerpt":"Let $P$ be a Delzant polytope. We show that the quantization of the corresponding toric manifold $X_{P}$ in toric K\\\"ahler polarizations and in the toric real polarization are related by analytic continuation of Hamiltonian flows evaluated at time $t = \\sqrt{-1} s$. We relate the quantization of $X_{P}$ in two different toric K\\\"ahler polarizations by taking the time-$\\sqrt{-1} s$ Hamiltonian \"flow\" of strongly convex functions on the moment polytope $P$. By taking $s$ to infinity, we obtain the quantization of $X_{P}$ in the (singular) real toric polarization.\n  Recall that $X_{P}$ has an ope"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2793","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"}