Pith Number

pith:L2BDBZRJ

pith:2026:L2BDBZRJUYU7QIRJE6GMMQCR4M

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On the Classification of Vaisman Manifolds with Vanishing First Basic Chern Class and Large First Betti Number

Lucas H. S. Gomes

Every Vaisman manifold with high first Betti number and vanishing first basic Chern class is diffeomorphic to a Kodaira-Thurston manifold.

arxiv:2604.04134 v2 · 2026-04-05 · math.DG

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Claims

C1strongest claim

We show that every Vaisman manifold with high first Betti number and vanishing first basic Chern class is diffeomorphic to a Kodaira-Thurston manifold. Furthermore, its complex structure is left-invariant, the characteristic foliation is regular, and the associated fibration is given by the Albanese map.

C2weakest assumption

The manifold is assumed to be Vaisman (i.e., locally conformal Kähler with parallel Lee form) and to satisfy the global topological conditions of high first Betti number together with vanishing first basic Chern class; if either the Vaisman condition or these numerical hypotheses fail, the diffeomorphism conclusion does not hold.

C3one line summary

Vaisman manifolds with high first Betti number and zero first basic Chern class are diffeomorphic to Kodaira-Thurston manifolds with left-invariant complex structure, regular foliation, and Albanese fibration.

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-22T01:04:01.517348Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5e8230e629a629f82229278cc64051e3345ee488c7dace7d4df4cc4881b3e2c9

Aliases

arxiv: 2604.04134 · arxiv_version: 2604.04134v2 · doi: 10.48550/arxiv.2604.04134 · pith_short_12: L2BDBZRJUYU7 · pith_short_16: L2BDBZRJUYU7QIRJ · pith_short_8: L2BDBZRJ

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/L2BDBZRJUYU7QIRJE6GMMQCR4M \
  | 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: 5e8230e629a629f82229278cc64051e3345ee488c7dace7d4df4cc4881b3e2c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "65277bda8f1103ace5f43f5244a6ed01d9adab610f05dfe523d8c0ceda96e2b2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2026-04-05T14:30:36Z",
    "title_canon_sha256": "27c7feefe6f179b68288618ba69010efe52d49bf95de5b1f15f91fefd845c0a3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.04134",
    "kind": "arxiv",
    "version": 2
  }
}