Pith Number

pith:3OUE5LHR

pith:2026:3OUE5LHRJNA73WJGFSBP7YIRWJ

not attested not anchored not stored refs resolved

Tilt-stability on singular schemes and Bogomolov-Gieseker-type inequalities

Tianle Mao, Zhiyu Liu

Tilt-stability extends to singular schemes and supports a generalized Bogomolov-Gieseker inequality conjecture for singular threefolds.

arxiv:2605.13808 v1 · 2026-05-13 · math.AG

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We generalize the framework of tilt-stability to singular schemes and formulate the generalized Bogomolov-Gieseker inequality conjecture of Bayer-Macrì-Toda for singular threefolds.

C2weakest assumption

The schemes are projective and the singularities satisfy conditions such as canonical Gorenstein Q-factorial for the verifications to apply.

C3one line summary

Tilt-stability is extended to singular schemes, a generalized Bogomolov-Gieseker conjecture is formulated and verified for certain singular threefolds, and stability conditions are constructed on relative Kuznetsov components.

References

16 extracted · 16 resolved · 2 Pith anchors

[1] Wall-crossing implies Brill–Noether: applications of stability conditions on surfaces 2015

[2] Sur le produit de vari\'et\'es localement factorielles ou Q-factorielles · arXiv:1104.1861

[3] Mukai bundles on Fano three- folds.arXiv preprint, arXiv:2402.07154,

[4] Mukai models of Fano varieties

Receipt and verification

First computed	2026-05-18T02:44:15.425634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dba84eacf14b41fdd9262c82ffe111b2717e7dfcdf234eb54fadb6c037a9ade7

Aliases

arxiv: 2605.13808 · arxiv_version: 2605.13808v1 · doi: 10.48550/arxiv.2605.13808 · pith_short_12: 3OUE5LHRJNA7 · pith_short_16: 3OUE5LHRJNA73WJG · pith_short_8: 3OUE5LHR

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3OUE5LHRJNA73WJGFSBP7YIRWJ \
  | 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: dba84eacf14b41fdd9262c82ffe111b2717e7dfcdf234eb54fadb6c037a9ade7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e738b28054bdb8a21e73f2064b87ea8af0bae4a0ef2e93d6fae423afb84e65b2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-13T17:36:44Z",
    "title_canon_sha256": "562651db2680299ccc1acf4b0a5097df1cf7e626db6ce5853305aa3671ee7e41"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13808",
    "kind": "arxiv",
    "version": 1
  }
}