Pith Number

pith:WIYYGW2Z

pith:2025:WIYYGW2ZXQIAKSFHADNMEP3B7N

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Existence of Conical Higher cscK Metrics on a Minimal Ruled Surface

Rajas Sandeep Sompurkar

Conical singularities along special divisors yield higher cscK metrics in every Kähler class on minimal ruled surfaces.

arxiv:2505.19257 v3 · 2025-05-25 · math.DG · math.CV

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Record completeness

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3 Author claim open · sign in to claim

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

If we allow our metrics to develop conical singularities along at least one of the two special divisors then we do get conical higher cscK metrics in each Kähler class by the momentum construction.

C2weakest assumption

The momentum construction extends to produce polyhomogeneous conical metrics that satisfy the higher cscK equation interpreted via currents of integration along the divisors, as stated in the abstract's description of the construction and global interpretation.

C3one line summary

Existence of conical higher cscK metrics is proven in every Kähler class on pseudo-Hirzebruch surfaces via momentum construction, with polyhomogeneous regularity and a conjectural cone-angle relation from the top log Bando-Futaki invariant.

References

42 extracted · 42 resolved · 1 Pith anchors

[1] Takahiro Aoi, Yoshinori Hashimoto and Kai Zheng.On UniformlogK-Stability for Constant Scalar Curvature K¨ ahler Cone Metrics. Commun. Anal. Geom.33(2025), no. 3, 701-767, DOI 10.4310/CAG.250730175404 2025 · doi:10.4310/cag.250730175404

[2] Shigetoshi Bando.An Obstruction for Chern Class Forms to be Harmonic. Kodai Math. Jour.29(2006), no. 3, 337-345, DOI 10.2996/kmj/1162478766 2006 · doi:10.2996/kmj/1162478766

[3] Barth, Klaus Hulek, Chris A

[4] and Hulek, Klaus and Peters, Chris A 2004 · doi:10.1007/978-3-642-57739-0

[5] Alan Taylor.A New Capacity for Plurisubharmonic Functions 1982 · doi:10.1007/bf02392348

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-03T02:05:41.116626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b231835b59bc100548a700dac23f61fb4f38c938ec0f5a167ff1a4cc0974f106

Aliases

arxiv: 2505.19257 · arxiv_version: 2505.19257v3 · doi: 10.48550/arxiv.2505.19257 · pith_short_12: WIYYGW2ZXQIA · pith_short_16: WIYYGW2ZXQIAKSFH · pith_short_8: WIYYGW2Z

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WIYYGW2ZXQIAKSFHADNMEP3B7N \
  | 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: b231835b59bc100548a700dac23f61fb4f38c938ec0f5a167ff1a4cc0974f106

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4c9a2435ea2c3a72185b2bffb7dabcdd8f6abfe43fbf341dddd97b6df75e44ee",
    "cross_cats_sorted": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2025-05-25T18:25:40Z",
    "title_canon_sha256": "88995bf81e8a908dd79a49f02e3a5f4ece463000c418eadbb11cbadb3d74795c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2505.19257",
    "kind": "arxiv",
    "version": 3
  }
}