Pith Number

pith:MEZUPMTR

pith:2024:MEZUPMTRNN54WMTGDHWB62UTCL

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On two families of Enriques categories over K3 surfaces

Ziqi Liu

Two families of Enriques categories over K3 surfaces yield moduli spaces of semistable objects that recover classical constructions such as double EPW sextics.

arxiv:2412.06921 v5 · 2024-12-09 · math.AG

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Claims

C1strongest 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.

C2weakest 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).

C3one 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.

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

Derived-natural automorphisms on Hilbert schemes of points on generic K3 surfaces

Receipt and verification

First computed	2026-06-09T01:05:04.329883Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

613347b2716b7bcb326619ec1f6a9312f5f3adfe717cd7d323e8098c73869b19

Aliases

arxiv: 2412.06921 · arxiv_version: 2412.06921v5 · doi: 10.48550/arxiv.2412.06921 · pith_short_12: MEZUPMTRNN54 · pith_short_16: MEZUPMTRNN54WMTG · pith_short_8: MEZUPMTR

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/MEZUPMTRNN54WMTGDHWB62UTCL \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 613347b2716b7bcb326619ec1f6a9312f5f3adfe717cd7d323e8098c73869b19

Canonical record JSON

{
  "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
  }
}