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pith:V2AMOHBH

pith:2026:V2AMOHBHG4SAMIVAEMB6NFYWLR

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Numerical characterizations for integral dependence of graded modules

Sudeshna Roy, Suprajo Das, Vijaylaxmi Trivedi

Adic and density functions give criteria for integral dependence of graded torsion-free modules.

arxiv:2605.14203 v1 · 2026-05-13 · math.AC · math.AG

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Claims

C1strongest claim

We construct adic, saturated and ε-density functions for a torsion-free module in a graded setup. Then we give some simple criteria for checking the integral dependence of two graded modules N⊆M in terms of various well-studied invariants.

C2weakest assumption

The constructions and criteria apply specifically to torsion-free modules in a graded setup; the abstract provides no indication of how the functions behave or whether the criteria extend when torsion is present or the grading is absent.

C3one line summary

New density functions and simple criteria are given to characterize integral dependence of graded modules via well-studied invariants.

References

20 extracted · 20 resolved · 0 Pith anchors

[1] Y. Cid-Ruiz. Polar multiplicities and integral dependence.International Mathematics Research Notices, 2024(17):12201–12218, 2024. 1 2024

[2] Y. Cid-Ruiz, C. Polini, and B. Ulrich. Multidegrees, families, and integral dependence.arXiv preprint arXiv:2405.07000, 2024. 1 2024

[3] Cutkosky,Asymptotic growth of saturated powers and epsilon multiplicityMath 2011

[4] Cutkosky,Asymptotic multiplicities of graded families of ideals and linear series, Advances in Mathematics, 264 (2014),55-113, Elsevier 2014

[5] S. Das, S. Roy, and V. Trivedi. Density functions for epsilon multiplicity and families of ideals.Journal of the London Mathematical Society. Second Series, 111(4):Paper No. e70155, 51, 2025. 1, 3, 5, 2025

Receipt and verification

First computed	2026-05-17T23:39:11.020872Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae80c71c2737240622a02303e697165c7d41b12c255579095519ca0725d4dfcb

Aliases

arxiv: 2605.14203 · arxiv_version: 2605.14203v1 · doi: 10.48550/arxiv.2605.14203 · pith_short_12: V2AMOHBHG4SA · pith_short_16: V2AMOHBHG4SAMIVA · pith_short_8: V2AMOHBH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/V2AMOHBHG4SAMIVAEMB6NFYWLR \
  | 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: ae80c71c2737240622a02303e697165c7d41b12c255579095519ca0725d4dfcb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6f522a98e9a07c3f7c4ab3f7f65a16e14cb46363163dce7f8d6130490ce45c7",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2026-05-13T23:40:28Z",
    "title_canon_sha256": "cf6899ccf2fcf063bdc72c9919c31453ce2b96b6bf3354d48593955c9a36e820"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14203",
    "kind": "arxiv",
    "version": 1
  }
}