{"paper":{"title":"Theory of multi-fans","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.SG","authors_text":"Akio Hattori, Mikiya Masuda","submitted_at":"2001-06-27T11:21:50Z","abstract_excerpt":"We introduce the notion of a multi-fan. It is a generalization of that of a fan in the theory of toric variety in algebraic geometry. Roughly speaking a toric variety is an algebraic variety with an action of algebraic torus of the same dimension as that of the variety, and a fan is a combinatorial object associated with the toric variety. Algebro-geometric properties of the toric variety can be described in terms of the associated fan. We develop a combinatorial theory of multi-fans and define ``topological invariants'' of a multi-fan. A smooth manifold with an action of a compact torus of ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0106229","kind":"arxiv","version":3},"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/0106229/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"}