{"paper":{"title":"On a Morelli type expression of cohomology classes of torus orbifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Akio Hattori","submitted_at":"2013-08-12T00:12:22Z","abstract_excerpt":"Let X be a complete toric variety of dimension n and \\del the fan in a lattice N associated to X. For each cone \\sigma of \\del there corresponds an orbit closure V(\\sigma) of the action of complex torus on X. The homology classes {[V(\\sigma)]| \\dim \\sigma=k} form a set of specified generators of H_{n-k}(X,Q). Then any x\\in H_{n-k}(X,Q) can be written in the form \\[ x=\\sum_{\\sigma\\in\\del_X, \\dim\\sigma=k}\\mu(x,\\sigma)[V(\\sigma)]. \\] A question occurs whether there is some canonical way to express \\mu(x,\\sigma). Morelli gave an answer when X is non-singular and at least for x= \\T_{n-k}(X) the Tod"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2439","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"}