{"paper":{"title":"On two families of Enriques categories over K3 surfaces","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"Two families of Enriques categories over K3 surfaces yield moduli spaces of semistable objects that recover classical constructions such as double EPW sextics.","cross_cats":[],"primary_cat":"math.AG","authors_text":"Ziqi Liu","submitted_at":"2024-12-09T19:08:28Z","abstract_excerpt":"This article studies the moduli spaces of semistable objects related to two families of Enriques categories over K3 surfaces, coming from quartic double solids and special Gushel-Mukai threefolds. In particular, some classic geometric constructions are recovered in a modular way, such as the double EPW sextic and cube associated with a general Gushel-Mukai surface, and the Beauville's birational involution on the Hilbert scheme of two points on a quartic K3 surface. In addition, we describe the singular loci in some moduli spaces of semistable objects and an explicit birational involution on O"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Some classic geometric constructions are recovered in a modular way, such as the double EPW sextic and cube associated with a general Gushel-Mukai surface, and the Beauville's birational involution on the Hilbert scheme of two points on a quartic K3 surface.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The categories arising from quartic double solids and special Gushel-Mukai threefolds are Enriques categories, and the moduli spaces of their semistable objects correspond to the stated classical geometric constructions (abstract, paragraph 1).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Studies moduli spaces for two families of Enriques categories over K3 surfaces from specific threefolds, recovering classical constructions modularly and providing a criterion for Enriques categories in the appendix.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Two families of Enriques categories over K3 surfaces yield moduli spaces of semistable objects that recover classical constructions such as double EPW sextics.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4219a70217dc0f2e63a03b2d37c90f48ab2e933f29d9938b262a207c8783c40a"},"source":{"id":"2412.06921","kind":"arxiv","version":5},"verdict":{"id":"24943df1-28df-41ba-98b3-46c1856b725c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-23T07:32:23.432949Z","strongest_claim":"Some classic geometric constructions are recovered in a modular way, such as the double EPW sextic and cube associated with a general Gushel-Mukai surface, and the Beauville's birational involution on the Hilbert scheme of two points on a quartic K3 surface.","one_line_summary":"Studies moduli spaces for two families of Enriques categories over K3 surfaces from specific threefolds, recovering classical constructions modularly and providing a criterion for Enriques categories in the appendix.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The categories arising from quartic double solids and special Gushel-Mukai threefolds are Enriques categories, and the moduli spaces of their semistable objects correspond to the stated classical geometric constructions (abstract, paragraph 1).","pith_extraction_headline":"Two families of Enriques categories over K3 surfaces yield moduli spaces of semistable objects that recover classical constructions such as double EPW sextics."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.06921/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":2,"snapshot_sha256":"b7d7f871a6cea3dbf1f81641d6cd13c01f6ec07c378ad94245d62e9d91ad8c9b"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}