Pith Number

pith:AEEUTBQE

pith:2026:AEEUTBQEUSTKYDDCA6GIUUO75E

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Moduli of Persson surfaces: The compactification via KSBA stable pairs and a generic global Torelli type theorem

Bin Nguyen, Hanlong Fang, Xian Wu, Zheng Zhang

Up to two possibilities, a generic smooth Persson surface can be recovered from the Hodge structure on the anti-invariant part of the second cohomology of its étale double cover together with the associated (Z/2Z)^5-action.

arxiv:2605.17223 v1 · 2026-05-17 · math.AG

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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

Up to two possibilities, a generic smooth Persson surface can be recovered from the Hodge structure on the anti-invariant part of the second cohomology of its étale double cover, together with the associated G̃=(Z/2Z)^5-action.

C2weakest assumption

The eight lines are general, so that the Galois cover yields a smooth canonically polarized surface and the KSBA wall-crossing analysis encounters no extra obstructions beyond the Q-Gorenstein ones computed in the paper.

C3one line summary

Constructs the KSBA compactification of moduli of Persson surfaces as (Z/2Z)^4-covers of P^2 and proves a generic global Torelli theorem from the anti-invariant Hodge structure on the etale double cover with (Z/2Z)^5 action.

References

67 extracted · 67 resolved · 2 Pith anchors

[1] Stable spherical varieties and their moduli 2006

[2] Wall crossing for moduli of stable log pairs 2023

[3] Carlson, and Domingo Toledo 2002

[4] Carlson, and Domingo Toledo 2011

[5] On lattice-polarized K3 surfaces, 2025 2025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:46.065727Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0109498604a4a6ac0c62078c8a51dfe91735284cdcfc959a1d7ac8127551f063

Aliases

arxiv: 2605.17223 · arxiv_version: 2605.17223v1 · doi: 10.48550/arxiv.2605.17223 · pith_short_12: AEEUTBQEUSTK · pith_short_16: AEEUTBQEUSTKYDDC · pith_short_8: AEEUTBQE

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AEEUTBQEUSTKYDDCA6GIUUO75E \
  | 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: 0109498604a4a6ac0c62078c8a51dfe91735284cdcfc959a1d7ac8127551f063

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af88123d1dec5ff1c8ed58ea216fd271c719192b4cb8fb4967aeb7fcbf0ede2a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2026-05-17T02:08:12Z",
    "title_canon_sha256": "69888d9b9ca52b312920d804efe428362aafe05676c80798263e96a6702d362f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17223",
    "kind": "arxiv",
    "version": 1
  }
}