{"paper":{"title":"Symplectic birational transformations of the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"J\\'er\\'emy Blanc","submitted_at":"2010-12-03T11:33:13Z","abstract_excerpt":"We study the group of symplectic birational transformations of the plane. It is proved that this group is generated by $\\mathrm{SL}(2,\\mathbb{Z})$, the torus and a special map of order $5$, as it was conjectured by A. Usnich.\n  Then we consider a special subgroup $H$, of finite type, defined over any field which admits a surjective morphism to the Thompson group of piecewise linear automorphisms of $\\mathbb{Z}^2$. We prove that the presentation for this group conjectured by Usnich is correct."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0706","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"}