{"paper":{"title":"A special Debarre-Voisin fourfold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jieao Song","submitted_at":"2021-06-24T19:29:50Z","abstract_excerpt":"Consider the finite simple group $\\mathbf{G}:=\\mathrm{PSL}(2,\\mathbf{F}_{11})$ of order 660, which has an irreducible representation $V_{10}$ of dimension 10. In this note, we study a special trivector ${\\sigma_0}\\in \\bigwedge^3V_{10}^\\vee$ that is $\\mathbf{G}$-invariant. Following the construction of Debarre-Voisin, we obtain a smooth hyperk\\\"ahler fourfold $X_6^{\\sigma_0}\\subset\\mathrm{Gr}(6,V_{10})$ with many symmetries. We will also look at the associated Peskine variety $X_1^{\\sigma_0}\\subset \\mathbf{P}(V_{10})$, which is highly symmetric as well and admits 55 isolated singular points. It"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.13287","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.13287/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"}