{"paper":{"title":"Weddle schemes","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Brian Harbourne, Giuseppe Favacchio, Juan Migliore, Justyna Szpond, Luca Chiantini, {\\L}ucja Farnik, Tomasz Szemberg","submitted_at":"2026-06-23T18:13:07Z","abstract_excerpt":"The classical Weddle surface is the locus of vertices of quadric cones through six points in $\\mathbb{P}^3$ in linear general position. Equivalently, it is the closure of the locus of centers of projection from which those six points map to six points on a plane conic. Motivated by this 1850 construction of T. Weddle, we introduce $d$-Weddle schemes for finite point sets $Z\\subset \\mathbb{P}^n$, defined by an analogous projection-to-degree-$d$ condition. Our main tool is Macaulay duality, which yields a natural multiplication map in an Artinian algebra defined by powers of linear forms. This v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25060","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.25060/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}