Pith Number

pith:T3W2CYZG

pith:2026:T3W2CYZGTIXYB4T2LQ5UW2O4BJ

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Quadratic Euler Characteristic of Geometrically Cyclic Branched Coverings

Louisa F. Br\"oring

For n-fold geometrically cyclic branched coverings of smooth projective schemes branched along a smooth subscheme with n invertible, the quadratic Euler characteristic of the cover is given by Euler classes on the base and branch locus via

arxiv:2605.13425 v1 · 2026-05-13 · math.AG

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Claims

C1strongest claim

For an n-fold geometrically cyclic branched covering Y of a smooth projective scheme X branched at a smooth closed subscheme Z with n invertible, the quadratic Euler characteristic of Y is computed in terms of certain Euler classes on X and Z using the quadratic Riemann-Hurwitz formula of Levine.

C2weakest assumption

That Levine's quadratic Riemann-Hurwitz formula applies directly to the geometrically cyclic branched coverings considered, with the given smoothness and projectivity hypotheses on X and Z and with n invertible in the base field.

C3one line summary

Quadratic Euler characteristic of geometrically cyclic branched coverings is computed from Euler classes on the base and branch locus via Levine's quadratic Riemann-Hurwitz formula, with explicit relations for odd n.

References

13 extracted · 13 resolved · 1 Pith anchors

[1] Euler classes: six-functors form- alism, dualities, integrality and linear subspaces of complete intersections 2020

[2] Finite Chow-Witt correspondences 2021 · arXiv:1412.2989

[3] Springer-Verlag, Berlin, 2000, pp 2000

[4] Duality, trace and transfer 1967

[5] Milnor-WittK-groups of local rings 2016

Receipt and verification

First computed	2026-05-18T02:44:47.275751Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9eeda163269a2f80f27a5c3b4b69dc0a72e6a59210f2d51e4150416e2eb11d95

Aliases

arxiv: 2605.13425 · arxiv_version: 2605.13425v1 · doi: 10.48550/arxiv.2605.13425 · pith_short_12: T3W2CYZGTIXY · pith_short_16: T3W2CYZGTIXYB4T2 · pith_short_8: T3W2CYZG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/T3W2CYZGTIXYB4T2LQ5UW2O4BJ \
  | 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: 9eeda163269a2f80f27a5c3b4b69dc0a72e6a59210f2d51e4150416e2eb11d95

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ada76ec044189a29e6a8c36ba6e68b77b553cd937a6f8835687f122f0d61dfa",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-13T12:20:04Z",
    "title_canon_sha256": "cb2a5f375427660da5bd56a2dad751236d37911df120323fb0a7b2c3b3a36c7a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13425",
    "kind": "arxiv",
    "version": 1
  }
}