Pith Number

pith:FPUHHLZD

pith:2024:FPUHHLZDQB4BY2WE7AF2F6UFMU

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On the rationality of some real threefolds

Alena Pirutka, Olivier Benoist

Some geometrically rational threefolds over real closed fields are irrational even when intermediate Jacobian obstructions vanish.

arxiv:2412.13624 v2 · 2024-12-18 · math.AG

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4 Citations 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

We obtain both negative and positive results, using unramified cohomology and birational rigidity techniques, as well as concrete rationality constructions.

C2weakest assumption

The real locus is connected and the intermediate Jacobian obstructions to rationality vanish for the geometrically rational three-dimensional conic and quadric surface bundles under study.

C3one line summary

The authors establish positive and negative rationality results for certain real threefolds that are conic or quadric surface bundles with connected real locus and vanishing intermediate Jacobian obstruction.

References

56 extracted · 56 resolved · 1 Pith anchors

[1] write newline

[2] M. Artin and D. Mumford, Some elementary examples of unirational varieties which are not rational, Proc. LMS 25 (1972), 75--95 1972

[3] Ambro, Quasi-log varieties, Tr 2003

[4] J\'on Kr. Arason, Cohomologische invarianten quadratischer F ormen , J. Algebra 36 (1975), no. 3, 448--491 1975

[5] A. A. Avilov, Existence of standard models of conic bundles over algebraically non-closed fields, Sb. Math. 205 (2014), no. 12, 1683--1695 2014

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

A rationality criterion for real Fano threefolds

Receipt and verification

First computed	2026-07-21T02:21:16.003197Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2be873af2380781c6ac4f80ba2fa8565128fa4f774831aa27ea7e4932a11f8eb

Aliases

arxiv: 2412.13624 · arxiv_version: 2412.13624v2 · doi: 10.48550/arxiv.2412.13624 · pith_short_12: FPUHHLZDQB4B · pith_short_16: FPUHHLZDQB4BY2WE · pith_short_8: FPUHHLZD

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FPUHHLZDQB4BY2WE7AF2F6UFMU \
  | 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: 2be873af2380781c6ac4f80ba2fa8565128fa4f774831aa27ea7e4932a11f8eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2081bf896626b5a11903841fea2de5849609cb3f64208d1aad392fd9a6422373",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2024-12-18T09:04:09Z",
    "title_canon_sha256": "23f2a51b192612c6a28a97d33a34e57ee90083671594409a19d5b70638c2d508"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.13624",
    "kind": "arxiv",
    "version": 2
  }
}