Pith Number

pith:3GU7XWAC

pith:2026:3GU7XWAC3ZDENUUXC2Q46UWRQ6

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Generic $\mathcal{A}$-finite determinacy and singularities of homogeneous polynomial mappings

J. V. Pissolato, M. A. S. Ruas, N. G. Grulha Jr.

Homogeneous polynomial mappings are generically A-finitely determined in dimensions 2 to 4.

arxiv:2605.17350 v1 · 2026-05-17 · math.AG

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\usepackage{pith}
\pithnumber{3GU7XWAC3ZDENUUXC2Q46UWRQ6}

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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

Using the strategy from Farnik, Jelonek and Ruas (2019), the authors extend and generalize key findings on generic properties and A-finite determinacy to dimensions greater than or equal to 2, though some properties can only be extended up to dimension 4.

C2weakest assumption

The geometric criterion for A-finite determinacy from the 2019 paper applies without modification to the higher-dimensional homogeneous cases considered here.

C3one line summary

Extends generic A-finite determinacy and singularity properties of homogeneous polynomial mappings from dimension 3 to dimensions >=2 (some up to 4) using geometric criteria from prior work.

References

11 extracted · 11 resolved · 0 Pith anchors

[1] V. I. Denilov, I. R. Shafarevich, and V. V. Shokurov.Algebraic Geometry I:, volume 23 ofEncyclopaedia Mathematical Sciences. Springer Berlin, Heidelberg, Berlin, 1994 1994

[2] M. Farnik, Z. Jelonek, and M. A. S. Ruas. Whitney theorem for complex polynomial mappings.Mathematische Zeitschrift, 295:1039–1065, 2020 2020

[3] M. Farnik, Z. Jelonek, and M. A. S. Ruas. FiniteA-determinacy of generic homogeneous map germs inC 3.Journal of the Mathematical Society of Japan, 73(1):211–220, 2021 2021

[4] M. E. Kazarian. Multisingularities, cobordisms, and enumerative geometry. Russian Math. Surveys, 58:665–724, 2003 2003

[5] J. N. Mather. Stability ofC ∞ mappings II: Infinitesimal stability implies stability. Annals of Mathematics, pages 254–291, 1969 1969

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:53.599423Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9a9fbd802de4646d29716a1cf52d187a98e637f5fd987da8c4e43c6fab826ad

Aliases

arxiv: 2605.17350 · arxiv_version: 2605.17350v1 · doi: 10.48550/arxiv.2605.17350 · pith_short_12: 3GU7XWAC3ZDE · pith_short_16: 3GU7XWAC3ZDENUUX · pith_short_8: 3GU7XWAC

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/3GU7XWAC3ZDENUUXC2Q46UWRQ6 \
  | 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: d9a9fbd802de4646d29716a1cf52d187a98e637f5fd987da8c4e43c6fab826ad

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b082374afd93a14d4caa4b9cab34ea3e56564cfb416b02b11d166775e2548de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-17T09:43:10Z",
    "title_canon_sha256": "d7c92c968267161bb8e0748d63a7d4d79221ec9ee2919bf5e78c43a8a3731e82"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17350",
    "kind": "arxiv",
    "version": 1
  }
}