{"paper":{"title":"The birational geometry of noncommutative surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.SI"],"primary_cat":"math.AG","authors_text":"Eric M. Rains","submitted_at":"2019-07-25T20:29:46Z","abstract_excerpt":"We show that any commutative rationally ruled surface with a choice of anticanonical curve admits a 1-parameter family of noncommutative deformations parametrized by the Jacobian of the anticanonical curve, and show that many standard facts from commutative geometry (blowups commute, Quot schemes are projective, etc.) carry over. The key new tool in studying these deformations is a relatively simple description of their derived categories and the relevant t-structures; this also allows us to establish nontrivial derived equivalences for deformations of elliptic surfaces. We also establish that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11301","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"}