{"paper":{"title":"Boundedness and $K^2$ for log surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Valery Alexeev","submitted_at":"1994-02-09T00:58:27Z","abstract_excerpt":"Let $\\epsilon, C$ be two positive real numbers, and $\\mathcal C \\subset \\mathbb R$ be a DCC (descending chain condition) set. Let $(X, B = \\sum b_j B_j)$ denote a projective surface with an $\\mathbb R$-divisor. Then\n  (1) The class $\\{X\\}$ of surfaces for which there exists a divisor $B$ such that $(X,B)$ is $\\epsilon$-log terminal and $-(K_X + B)$ is nef (excluding only those for which at the same time $K_X\\equiv 0$, $B=0$, and $X$ has at worst Du Val singularities), is bounded.\n  (2) The set $\\{(K_X + B)^2\\}$ of squares for the semi log canonical pairs $(X, B)$ with ample $K_X + B$ and $b_j "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9402007","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":""},"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"}