{"paper":{"title":"Linear systems on the blow-up of (P^1)^n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Antonio Laface, Joaqu\\'in Moraga","submitted_at":"2014-01-26T21:18:52Z","abstract_excerpt":"In this note we study linear systems on the blow-up of $(\\mathbb{P}^1)^n$ at $r$ points in very general position. We prove that the fibers of the projections $(\\mathbb{P}^1)^n \\rightarrow (\\mathbb{P}^1)^s, 1\\leq s \\leq n-1$ can give contribution to the speciality of the linear system. This allows us to give a new definition of expected dimension of a linear system in $(\\mathbb{P}^1)^n$ which we call fiber dimension. Finally, we state a conjecture about linear systems on $(\\mathbb{P}^1)^3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6692","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"}