{"paper":{"title":"Optimal and maximal singular curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Annamaria Iezzi (I2M), IMATH), Yves Aubry (I2M","submitted_at":"2015-10-07T07:51:39Z","abstract_excerpt":"Using an Euclidean approach, we prove a new upper bound for the number of closed points of degree 2 on a smooth absolutely irreducible projective algebraic curve defined over the finite field $\\mathbb F\\_q$.This bound enables us to provide explicit conditions on $q, g$ and $\\pi$  for the non-existence of absolutely irreducible projective algebraic curves defined over $\\mathbb F\\_q$ of geometric genus $g$, arithmetic genus $\\pi$ and with $N\\_q(g)+\\pi-g$ rational points.Moreover, for $q$ a square, we study the set of pairs $(g,\\pi)$ for which there exists a maximal absolutely irreducible project"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01853","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"}