Pith Number

pith:M7SCCEOV

pith:2026:M7SCCEOVMLPMPSSICJVTMITZ26

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$\mathbb T$-homogeneous locally nilpotent derivations of trinomial algebras

Kirill Rassolov, Timofey Krasikov

Trinomial algebras have their T-homogeneous locally nilpotent derivations fully described.

arxiv:2605.17670 v1 · 2026-05-17 · math.AG · math.AC

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Claims

C1strongest claim

We describe those locally nilpotent derivations of trinomial algebras homogeneous under a natural torus action of complexity one.

C2weakest assumption

Trinomial algebras are commutative finitely generated algebras given by a system of compatible relations each of which is a polynomial with three terms, and they arise as the Cox rings of varieties admitting a torus action of complexity one.

C3one line summary

The paper classifies T-homogeneous locally nilpotent derivations on trinomial algebras arising as Cox rings of complexity-one torus actions.

References

20 extracted · 20 resolved · 1 Pith anchors

[1] Altmann K., Hausen J.,Polyhedral divisors and algebraic torus actions, Math. Ann.334(2006), 3, 557–607 2006

[2] V.,On factoriality of Cox rings, Math 2009

[3] Arzhantsev I.,On rigidity of factorial trinomial hypersurfaces, Internat. J. Algebra Comput.26(2016), 5, 1061–1070 2016

[4] Arzhantsev I., Derenthal U., Hausen J., Laface A.,Cox Rings, Cambridge Studies in Advanced Mathematics 144, Cambridge Univ. Press, Cambridge, 2014. T-HOMOGENEOUS LOCALLY NILPOTENT DERIV ATIONS OF TRIN 2014

[5] J.61 (2012), 4, 731–762 2012

Formal links

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Receipt and verification

First computed	2026-05-20T00:04:51.883340Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67e42111d562dec7ca48126b362279d7b76f8241cf32630aa34de4f806719ab3

Aliases

arxiv: 2605.17670 · arxiv_version: 2605.17670v1 · doi: 10.48550/arxiv.2605.17670 · pith_short_12: M7SCCEOVMLPM · pith_short_16: M7SCCEOVMLPMPSSI · pith_short_8: M7SCCEOV

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/M7SCCEOVMLPMPSSICJVTMITZ26 \
  | 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: 67e42111d562dec7ca48126b362279d7b76f8241cf32630aa34de4f806719ab3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f55f42dbc8de87bf30dc143e21a4450fbea947b1b6a7b1fc31a72b716693a23a",
    "cross_cats_sorted": [
      "math.AC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-17T22:03:59Z",
    "title_canon_sha256": "79a86e22adc145533dc27fcd11b0aa9eb6ff9f4c2f7392b47ddf247932f4a589"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17670",
    "kind": "arxiv",
    "version": 1
  }
}