{"paper":{"title":"Classifying Toric and Semitoric Fans by Lifting Equations from ${\\rm SL}_2({\\mathbb Z})$","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.AG","math.DG","math.GR"],"primary_cat":"math.SG","authors_text":"\\'Alvaro Pelayo, Daniel M. Kane, Joseph Palmer","submitted_at":"2015-02-26T19:48:30Z","abstract_excerpt":"We present an algebraic method to study four-dimensional toric varieties by lifting matrix equations from the special linear group ${\\rm SL}_2({\\mathbb Z})$ to its preimage in the universal cover of ${\\rm SL}_2({\\mathbb R})$. With this method we recover the classification of two-dimensional toric fans, and obtain a description of their semitoric analogue. As an application to symplectic geometry of Hamiltonian systems, we give a concise proof of the connectivity of the moduli space of toric integrable systems in dimension four, recovering a known result, and extend it to the case of semitoric "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07698","kind":"arxiv","version":6},"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"}