{"paper":{"title":"Virtual invariants from the non-associative Hilbert scheme","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Felix Minddal, Gergely B\\'erczi","submitted_at":"2025-12-12T13:16:14Z","abstract_excerpt":"We introduce a non-associative model for the Hilbert scheme of points in arbitrary dimension. We define a smooth ambient space, which we call the non-associative Hilbert scheme, containing the classical nested Hilbert scheme $\\mathrm{NHilb}^{\\underline{d}}(\\mathbb{A}^n)$ as the associativity, cut out by an explicit section of an associativity bundle. This construction yields canonical perfect obstruction theories and virtual fundamental classes on $\\mathrm{NHilb}^{\\underline{d}}(\\mathbb{A}^n)$ for all $(n,\\underline d)$. Using virtual localization, we obtain closed formulas for these virtual c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.11538","kind":"arxiv","version":3},"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/2512.11538/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"}