Pith Number

pith:BS5RURPL

pith:2025:BS5RURPLTUMJMEDSMV6IIHFDS4

not attested not anchored not stored refs pending

Weak del Pezzo surfaces are characterized by the existence of $2$-tilting bundles

Ryu Tomonaga

A smooth projective surface admits a 2-tilting bundle if and only if it is a weak del Pezzo surface.

arxiv:2510.26199 v3 · 2025-10-30 · math.AG · math.AC · math.RA · math.RT

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\pithnumber{BS5RURPLTUMJMEDSMV6IIHFDS4}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

a smooth projective surface admits a 2-tilting bundle if and only if it is a weak del Pezzo surface. Moreover, if a d-dimensional smooth proper variety admits a d-tilting bundle, then it is weak Fano.

C2weakest assumption

The setting is restricted to smooth projective surfaces (or smooth proper varieties in higher dimensions) over an algebraically closed field, as required for the definitions of tilting bundles and weak del Pezzo surfaces to apply in the standard way (stated in the main result and the conjecture context).

C3one line summary

A smooth projective surface admits a 2-tilting bundle if and only if it is a weak del Pezzo surface.

Cited by

1 paper in Pith

Higher representation infinite algebras and toric Fano stacks of Picard number one or two

Receipt and verification

First computed	2026-05-27T01:05:39.409535Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0cbb1a45eb9d18961072657c841ca3973e41e5700418f194504946b47fc405b2

Aliases

arxiv: 2510.26199 · arxiv_version: 2510.26199v3 · doi: 10.48550/arxiv.2510.26199 · pith_short_12: BS5RURPLTUMJ · pith_short_16: BS5RURPLTUMJMEDS · pith_short_8: BS5RURPL

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BS5RURPLTUMJMEDSMV6IIHFDS4 \
  | 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: 0cbb1a45eb9d18961072657c841ca3973e41e5700418f194504946b47fc405b2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5d75c4ce44d14029318996be10b8f4ba6da13265d43cce193eb273e55892d581",
    "cross_cats_sorted": [
      "math.AC",
      "math.RA",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2025-10-30T07:19:21Z",
    "title_canon_sha256": "397587797bf2d78509b06926dc0699305e36497511623a72c9efb5fea30815aa"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.26199",
    "kind": "arxiv",
    "version": 3
  }
}