{"paper":{"title":"Hyperelliptic curves of genus 3 with prescribed automorphism group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"D. Sevilla, J. Gutierrez, T. Shaska","submitted_at":"2012-09-13T15:50:44Z","abstract_excerpt":"We study genus 3 hyperelliptic curves which have an extra involution. The locus $\\L_3$ of these curves is a 3-dimensional subvariety in the genus 3 hyperelliptic moduli $\\H_3$. We find a birational parametrization of this locus by affine 3-space. For every moduli point $\\p \\in \\H_3$ such that $|\\Aut (\\p)|>2$, the field of moduli is a field of definition. We provide a rational model of the curve over its field of moduli for all moduli points $\\p \\in \\H_3$ such that $|\\Aut(\\p)|>4$. This is the first time that such a rational model of these curves appears in the literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2938","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"}