{"paper":{"title":"A note on Harris Morrison sweeping families of maximal gonality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Francesco Zucconi, Valentina Beorchia","submitted_at":"2013-02-04T09:08:16Z","abstract_excerpt":"Harris and Morrison constructed semistable families f:F \\to Y of k-gonal curves of genus g such that for every k the corresponding modular curves give a sweeping family in the k-gonal locus in the moduli space. Their construction depends on the choice of a smooth curve X. We show that if the genus g(X) is sufficiently high with respect to g, then the ratio K_F^2 / \\chi(O_F) is 8 asymptotically with respect to g(X). We show also that if the gonality is maximal and some conjectured estimates of Harris and Morrison hold, the slope of the fibration f: F\\to Y is 12 asymptotically with respect to g "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0620","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"}