{"paper":{"title":"Automorphisms of the moduli space of smooth cubic surfaces and its fundamental group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic.","cross_cats":["math.GR","math.GT"],"primary_cat":"math.AG","authors_text":"Ariyan Javanpeykar, Benson Farb, Gregorio Baldi, Matthew Stover","submitted_at":"2026-05-15T21:54:13Z","abstract_excerpt":"Let $\\mathcal{C}$ be the moduli space of smooth complex cubic surfaces and let $\\pi_1(\\mathcal{C})$ be its (orbifold) fundamental group. We prove that the ``divisor subgroup'' of $\\pi_1(\\mathcal{C})$ is characteristic. This can be interpreted as saying that the group theory of $\\pi_1(\\mathcal{C})$ ``remembers'' the divisor of nodal cubic surfaces. We deduce from this group-theoretic result and some basic complex analysis that $\\mathcal{C}$ has no nontrivial biholomorphic automorphisms as complex analytic orbifold."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that the ``divisor subgroup'' of π₁(C) is characteristic. This can be interpreted as saying that the group theory of π₁(C) ``remembers'' the divisor of nodal cubic surfaces. We deduce from this group-theoretic result and some basic complex analysis that C has no nontrivial biholomorphic automorphisms as complex analytic orbifold.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The deduction that the characteristic property of the divisor subgroup, together with basic complex analysis, suffices to rule out all nontrivial biholomorphic automorphisms of C as an orbifold; this relies on an unstated but load-bearing identification of what constitutes a biholomorphic automorphism in the orbifold category and on the precise definition of the divisor subgroup being invariant under the relevant group actions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic, implying the space has no nontrivial biholomorphic automorphisms.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"76c457db597cbc5dcfa6fe4abc0107d3b566cf9287ba7655b2db69284c5a53d1"},"source":{"id":"2605.16658","kind":"arxiv","version":1},"verdict":{"id":"7984d9d6-9ef4-435e-94ae-c7dc688ad142","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T20:40:52.839112Z","strongest_claim":"We prove that the ``divisor subgroup'' of π₁(C) is characteristic. This can be interpreted as saying that the group theory of π₁(C) ``remembers'' the divisor of nodal cubic surfaces. We deduce from this group-theoretic result and some basic complex analysis that C has no nontrivial biholomorphic automorphisms as complex analytic orbifold.","one_line_summary":"The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic, implying the space has no nontrivial biholomorphic automorphisms.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The deduction that the characteristic property of the divisor subgroup, together with basic complex analysis, suffices to rule out all nontrivial biholomorphic automorphisms of C as an orbifold; this relies on an unstated but load-bearing identification of what constitutes a biholomorphic automorphism in the orbifold category and on the precise definition of the divisor subgroup being invariant under the relevant group actions.","pith_extraction_headline":"The divisor subgroup of the orbifold fundamental group of the moduli space of smooth cubic surfaces is characteristic."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.16658/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T21:01:19.303010Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T20:51:13.496580Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:01:56.399967Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T18:33:26.519602Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ad24176442b57fa83908058f84137615c0ea34f3da23e137ee38e96f5fff8ba2"},"references":{"count":15,"sample":[{"doi":"","year":2002,"title":"D. Allcock, J. A. Carlson, and D. Toledo. The complex hyperbolic geometry of the moduli space of cubic surfaces. J. Algebr. Geom., 11(4):659–724, 2002","work_id":"87ea9e12-dd7c-4a94-8033-ed273a8761a9","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2000,"title":"D. Allcock, J. A. Carlson, and D. Toledo. Orthogonal complex hyperbolic arrangements. In Symposium in Honor of C. H. Clemens (Salt Lake City, UT, 2000) , volume 312 of Contemp. Math. , pages 1–8. Amer","work_id":"a1f4ed53-0023-4d8d-a9b7-bc43927f9467","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1964,"title":"W. L. Baily, Jr. and A. Borel. On the compactification of arithmetically defined quotients of bounded symmetric domains. Bull. Amer. Math. Soc. , 70:588–593, 1964","work_id":"b1c33ebc-fe3d-4440-a1d9-0d829b062477","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1997,"title":"W. Bosma, J. Cannon, and C. Playoust. The Magma algebra system. I. The user language. J. Symbolic Comput., 24(3-4):235–265, 1997. Computational algebra and number theory (London, 1993)","work_id":"02d7e853-bfbd-441a-b7bb-7cc80b92a035","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1999,"title":"M. R. Bridson and A. Haefliger. Metric spaces of non-positive curvature, volume 319 of Grundlehren Math. Wiss. Berlin: Springer, 1999","work_id":"392c47f9-e253-4727-a9be-ace2c78a2eb4","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":15,"snapshot_sha256":"f9639b6b71acee0754b86fd0970b00cc455647dcd0f46b20922b692d5d39434c","internal_anchors":0},"formal_canon":{"evidence_count":1,"snapshot_sha256":"ea64dc2f5611a18303a17153cac9d1d526e345fdb291b12108602d2b96ede072"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}