{"paper":{"title":"On minimal rational elliptic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Antonio Laface, Damiano Testa","submitted_at":"2015-02-01T15:53:13Z","abstract_excerpt":"We construct $13$ projective $\\mathbb{Q}$-factorial Fano toric varieties and show that for any minimal rational elliptic surface $X$ there is one such toric variety $Z_X$ and a divisor class $\\delta_X\\in {\\rm Cl}(Z_X)$ such that the number of $(-1)$-curves of $X$ equals the dimension of the Riemann-Roch space of $\\delta_X$. As an application we give the number of $(-1)$-curves of any such elliptic fibration of Halphen index $2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.00275","kind":"arxiv","version":2},"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"}