{"paper":{"title":"Support theorem of universal compactified Jacobians","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"Every summand in the decomposition of the pushforward of the intersection cohomology sheaf from the universal compactified Jacobian has full support over the moduli space of curves.","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yifan Wu","submitted_at":"2026-05-04T19:25:23Z","abstract_excerpt":"We prove a full support theorem for the relative good moduli space of the universal compactified Jacobian $\\bar{\\pi}\\colon \\overline{J}_{g,n}^{d,\\phi}\\to \\overline{\\mathcal{M}}_{g,n}$, showing that every direct summand appearing in the BBDG decomposition of $\\mathrm{R}\\bar{\\pi}_*\\mathrm{IC}(\\overline{J}_{g,n}^{d,\\phi})$ has full support on the base $\\overline{\\mathcal{M}}_{g,n}$. Moreover, we explicitly describe this decomposition governed by the derived pushforward of the constant sheaf on the universal curve.\n  The first proof synthesizes Maulik and Shen's generalization of Ng\\^{o}'s support"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove a full support theorem for the relative good moduli space of the universal compactified Jacobian π̄ : J̄_{g,n}^{d,φ} → M̄_{g,n}, showing that every direct summand appearing in the BBDG decomposition of Rπ̄_* IC(J̄_{g,n}^{d,φ}) has full support on the base M̄_{g,n}.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The stability condition φ and degree d are chosen so that the good moduli space morphism exists and the intersection cohomology sheaf behaves well under the cited decomposition and support theorems; the abstract does not specify the precise range of (g,n,d,φ) for which this holds.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Every direct summand in the BBDG decomposition of Rπ_* IC of the universal compactified Jacobian has full support on the base moduli space of curves, with the decomposition governed by the pushforward of the constant sheaf on the universal curve.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Every summand in the decomposition of the pushforward of the intersection cohomology sheaf from the universal compactified Jacobian has full support over the moduli space of curves.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"e7767a53e0af04ac5d4d1a0ae7c122f7a4703c20af3ecb02455f96c7aff0cf36"},"source":{"id":"2605.03097","kind":"arxiv","version":2},"verdict":{"id":"7aca147f-a9f2-4b36-a267-c9e337c8b399","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T02:08:10.112378Z","strongest_claim":"We prove a full support theorem for the relative good moduli space of the universal compactified Jacobian π̄ : J̄_{g,n}^{d,φ} → M̄_{g,n}, showing that every direct summand appearing in the BBDG decomposition of Rπ̄_* IC(J̄_{g,n}^{d,φ}) has full support on the base M̄_{g,n}.","one_line_summary":"Every direct summand in the BBDG decomposition of Rπ_* IC of the universal compactified Jacobian has full support on the base moduli space of curves, with the decomposition governed by the pushforward of the constant sheaf on the universal curve.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The stability condition φ and degree d are chosen so that the good moduli space morphism exists and the intersection cohomology sheaf behaves well under the cited decomposition and support theorems; the abstract does not specify the precise range of (g,n,d,φ) for which this holds.","pith_extraction_headline":"Every summand in the decomposition of the pushforward of the intersection cohomology sheaf from the universal compactified Jacobian has full support over the moduli space of curves."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.03097/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T14:37:08.345748Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T02:01:21.875696Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:43:42.925900Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ab02d4210299bc8ae698a9814c61429131d704f27759c73f9a59d8fb1daade34"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}