{"paper":{"title":"Algebraic curves with many automorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gabor Korchmaros, Massimo Giulietti","submitted_at":"2017-02-28T15:06:21Z","abstract_excerpt":"Let $X$ be a (projective, geometrically irreducible, nonsingular) algebraic curve of genus $g \\ge 2$ defined over an algebraically closed field $K$ of odd characteristic $p$. Let $Aut(X)$ be the group of all automorphisms of $X$ which fix $K$ element-wise. It is known that if $|Aut(X)|\\geq 8g^3$ then the $p$-rank (equivalently, the Hasse-Witt invariant) of $X$ is zero. This raises the problem of determining the (minimum-value) function $f(g)$ such that whenever $|Aut(X)|\\geq f(g)$ then $X$ has zero $p$-rank. For {\\em{even}} $g$ we prove that $f(g)\\leq 900 g^2$. The {\\em{odd}} genus case appear"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08812","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"}