{"paper":{"title":"The Halphen cubics of order two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Brian Harbourne, Joaquim Ro\\'e, Thomas Bauer, Tomasz Szemberg","submitted_at":"2016-03-14T21:20:22Z","abstract_excerpt":"For each $m\\ge 1$, Roulleau and Urz\\'ua give an implicit construction of a configuration of $4(3m^2-1)$ complex plane cubic curves. This construction was crucial for their work on surfaces of general type. We make this construction explicit by proving that the Roulleau-Urz\\'ua configuration consists precisely of the Halphen cubics of order $m$, and we determine specific equations of the cubics for $m=1$ (which were known) and for $m=2$ (which are new)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04480","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"}