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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","authors_text":"Ziqi Liu","cross_cats":[],"headline":"Two families of Enriques categories over K3 surfaces yield moduli spaces of semistable objects that recover classical constructions such as double EPW sextics.","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AG","submitted_at":"2024-12-09T19:08:28Z","title":"On two families of Enriques categories over K3 surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.06921","kind":"arxiv","version":5},"verdict":{"created_at":"2026-05-23T07:32:23.432949Z","id":"24943df1-28df-41ba-98b3-46c1856b725c","model_set":{"reader":"grok-4.3"},"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","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.","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.","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)."}},"verdict_id":"24943df1-28df-41ba-98b3-46c1856b725c"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d09b7d4a779f1662be7c5b3245782a6b7f0d6b28e16a6094225fe5ff7d58da55","target":"record","created_at":"2026-06-09T01:05:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"55ba220f69a396c1e9ae3f3a0b961445ece967eb6c5fb9ca68cbaca736558b43","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AG","submitted_at":"2024-12-09T19:08:28Z","title_canon_sha256":"c78d53dbbacab47c7e695d33ff93085963b6218c55e77e4f477cad2909aa8344"},"schema_version":"1.0","source":{"id":"2412.06921","kind":"arxiv","version":5}},"canonical_sha256":"613347b2716b7bcb326619ec1f6a9312f5f3adfe717cd7d323e8098c73869b19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"613347b2716b7bcb326619ec1f6a9312f5f3adfe717cd7d323e8098c73869b19","first_computed_at":"2026-06-09T01:05:04.329883Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:04.329883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W3CN8Yt7sXZjZE4rYFn8fiwjCl5O2DS/DEiQBHZp5rs5pb+lMkR1soEzCQA7cHCFGbkStiUKvxQquPeBBx5KCA==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:04.330397Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.06921","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d09b7d4a779f1662be7c5b3245782a6b7f0d6b28e16a6094225fe5ff7d58da55","sha256:9827ddc73b4696d8307c1cbb05e0a5eba22bcdd2b1c90d5bd3b23bd34b9adf1f"],"state_sha256":"23b63a36fb3c9f7af1bf3480f1dbb4e442af915c3b5e299994f7844c2a4af038"}