{"paper":{"title":"Moduli of Persson surfaces: The compactification via KSBA stable pairs and a generic global Torelli type theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"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.","cross_cats":[],"primary_cat":"math.AG","authors_text":"Bin Nguyen, Hanlong Fang, Xian Wu, Zheng Zhang","submitted_at":"2026-05-17T02:08:12Z","abstract_excerpt":"We study a family of canonically polarized surfaces introduced by Persson, which arise as Galois $G=(\\mathbb{Z}/2\\mathbb{Z})^4$-covers of $\\mathbf{P}^2$ branched along eight general lines. For this family, we construct the compactified moduli space and explicitly describe the stable degenerations in the sense of Koll\\'ar, Shepherd-Barron, and Alexeev (KSBA) via stable pairs of weighted hyperplane arrangements. By computing the $\\mathbb{Q}$-Gorenstein obstructions and using the KSBA wall crossings, we show that the resulting compactified moduli stack is smooth. Furthermore, we establish a gener"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"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.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5b0f995477b517703bb24c7410636639a5690af1ee21dba8bed64fc902083616"},"source":{"id":"2605.17223","kind":"arxiv","version":1},"verdict":{"id":"fc14d39a-7cb3-499a-8007-2d84f92f76bb","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T23:23:17.443984Z","strongest_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.","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"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."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17223/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:31:20.368367Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:31:18.354557Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T22:01:57.913704Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.807853Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"e0207c68ef09460c845ca1caf57f8f251c54adcc6be87dbe2ccaf1b59f7fdf8f"},"references":{"count":67,"sample":[{"doi":"","year":2006,"title":"Stable spherical varieties and their moduli","work_id":"9007a089-5eed-4ae4-b0fd-8c04537c2732","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2023,"title":"Wall crossing for moduli of stable log pairs","work_id":"15ef5a92-586a-48d4-b16c-aad3354a9f7e","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2002,"title":"Carlson, and Domingo Toledo","work_id":"65aaf65a-da84-4acc-8fbf-9d0e1ff74789","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2011,"title":"Carlson, and Domingo Toledo","work_id":"a5c4c33c-49af-4465-9064-b24d4f893a2d","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2025,"title":"On lattice-polarized K3 surfaces, 2025","work_id":"ec874a60-2bcc-41af-b21d-b46a3e3e1d14","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":67,"snapshot_sha256":"d2913f48305b1337ad4256a701326919510ac5fd169232a6ced3592f5c8ca9e6","internal_anchors":2},"formal_canon":{"evidence_count":2,"snapshot_sha256":"7b4f5db566be44b91dcdecf8401e33a7a2c08c8baa14f0905e441835470993b3"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}