Pith Number

pith:7HYR2X64

pith:2026:7HYR2X64ZYZPUF2TMZUN225RN6

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A result on the generic Picard number of surfaces in fake weighted projective 3-spaces

Julius Giesler

A criterion based on edge degenerations shows that certain generic nondegenerate surfaces in fake weighted projective 3-spaces have Picard number greater than 1.

arxiv:2604.25709 v2 · 2026-04-28 · math.AG

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\usepackage{pith}
\pithnumber{7HYR2X64ZYZPUF2TMZUN225RN6}

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Record completeness

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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

We give a criterion for certain generic nondegenerate surfaces in a fake weighted projective 3-space to have Picard number >1.

C2weakest assumption

That degenerations along an edge permit reliable tracking of the geometric genus and that vanishing cohomology classes produce a rational Picard class independent of the canonical divisor.

C3one line summary

A criterion is established for generic nondegenerate surfaces in fake weighted projective 3-spaces to have Picard number >1 via edge degenerations, genus tracking, and vanishing cohomology classes yielding an extra rational Picard class.

Receipt and verification

First computed	2026-06-02T02:04:53.492780Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9f11d5fdcce32fa17536668dd6bb16fa25afeeb209a1bfbfd252ca90621faaa

Aliases

arxiv: 2604.25709 · arxiv_version: 2604.25709v2 · doi: 10.48550/arxiv.2604.25709 · pith_short_12: 7HYR2X64ZYZP · pith_short_16: 7HYR2X64ZYZPUF2T · pith_short_8: 7HYR2X64

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/7HYR2X64ZYZPUF2TMZUN225RN6 \
  | 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: f9f11d5fdcce32fa17536668dd6bb16fa25afeeb209a1bfbfd252ca90621faaa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07e7e35cf21cf710d4d4352e58b3f178295ad95ea992b4294b3ff5a8ba976142",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-04-28T14:34:30Z",
    "title_canon_sha256": "64a0c8ffb063d018756fce62ba0f5e1f766c3ca8235a94a4a9f46a5beabedcb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25709",
    "kind": "arxiv",
    "version": 2
  }
}