{"paper":{"title":"Bounding singular surfaces via Chern numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Joaqu\\'in Moraga","submitted_at":"2017-04-30T00:12:26Z","abstract_excerpt":"We prove the existence of a bound on the number of steps of the minimal model program for singular surfaces in terms of discrepancies and top Chern numbers. As an application, we prove that given $R\\in\\mathbb{R}$ and $\\epsilon\\in (0,1)$, the class $\\mathcal{F}(R,\\epsilon)$ of $2$-dimensional pairs $(X,D)$ of general type with $\\epsilon$-klt singularities, $D$ with standard coefficients, and $4c_2(X,D)-c_1^2(X,D)\\leq R$, forms a bounded family."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00256","kind":"arxiv","version":4},"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"}