{"paper":{"title":"Degeneration of Kaehler structures and half-form quantization of toric varieties","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":"2010-11-15T12:42:32Z","abstract_excerpt":"We study the half-form Kaehler quantization of a smooth symplectic toric manifold $(X,\\omega)$, such that $[\\omega/2\\pi]-c_{1}(X)/2 \\in H^{2}(X,{\\mathbb{Z}})$ and is nonnegative. We define the half-form corrected quantization of $(X,\\omega)$ to be given by holomorphic sections of a certain hermitian line bundle $L\\rightarrow X$ with Chern class $[\\omega/ 2\\pi]-c_{1}(X)/2$. These sections then correspond to integral points of a \"corrected\" polytope $P_{L}$ with integral vertices. For a suitably translated moment polytope $P_{X}$ for $(X,\\omega)$, we have that $P_{L}\\subset P_{X}$ is obtained fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3363","kind":"arxiv","version":2},"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"}