{"paper":{"title":"Holomorphic disks and GIT quotients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Moduli spaces of holomorphic disks correspond between a G-invariant Lagrangian and its quotient in the GIT quotient, allowing derivation of the quotient disk potential via the semistable disk potential.","cross_cats":["math.AG"],"primary_cat":"math.SG","authors_text":"Yoosik Kim","submitted_at":"2026-05-17T07:20:14Z","abstract_excerpt":"Let $G$ be a connected compact Lie group and let $\\mathbb{G}$ be its complexification. In this paper, we establish a correspondence between the moduli spaces of holomorphic disks bounded by a $G$-invariant Lagrangian submanifold $L \\subseteq X$ and those bounded by its quotient $L/G$ in the GIT quotient $X \\mathbin{/\\mkern-6mu/} \\mathbb{G}$. Under suitable positivity and topological assumptions, we derive a computationally effective formula for the disk potential of $L/G$ from that of $L$ via the {semistable disk potential}, which reflects the choice of a level set of a value of the moment map"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We establish a correspondence between the moduli spaces of holomorphic disks bounded by a G-invariant Lagrangian submanifold L ⊆ X and those bounded by its quotient L/G in the GIT quotient X//G. Under suitable positivity and topological assumptions, we derive a computationally effective formula for the disk potential of L/G from that of L via the semistable disk potential.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The positivity and topological assumptions on the Lagrangian submanifold L and the group action that are required for the moduli space correspondence and the derivation of the disk potential formula to hold (as stated in the abstract).","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Establishes correspondence between holomorphic disk moduli spaces for G-invariant Lagrangians and their GIT quotients, yielding a formula for the quotient disk potential via semistable disk potential.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Moduli spaces of holomorphic disks correspond between a G-invariant Lagrangian and its quotient in the GIT quotient, allowing derivation of the quotient disk potential via the semistable disk potential.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"7415d7019bfc07d681710d820965c7571c341258b0fc8278c79de03ce016baa7"},"source":{"id":"2605.17298","kind":"arxiv","version":1},"verdict":{"id":"1aa0558c-be78-4b95-8e36-38e3e5fe758f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T23:06:29.840638Z","strongest_claim":"We establish a correspondence between the moduli spaces of holomorphic disks bounded by a G-invariant Lagrangian submanifold L ⊆ X and those bounded by its quotient L/G in the GIT quotient X//G. Under suitable positivity and topological assumptions, we derive a computationally effective formula for the disk potential of L/G from that of L via the semistable disk potential.","one_line_summary":"Establishes correspondence between holomorphic disk moduli spaces for G-invariant Lagrangians and their GIT quotients, yielding a formula for the quotient disk potential via semistable disk potential.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The positivity and topological assumptions on the Lagrangian submanifold L and the group action that are required for the moduli space correspondence and the derivation of the disk potential formula to hold (as stated in the abstract).","pith_extraction_headline":"Moduli spaces of holomorphic disks correspond between a G-invariant Lagrangian and its quotient in the GIT quotient, allowing derivation of the quotient disk potential via the semistable disk potential."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17298/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T23:31:20.164761Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T23:13:08.694777Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T22:01:57.805952Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T21:33:23.762106Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"95139875a293aa29421ed23119e18cdad084ee977ce09a67d6cbc650751f2ca7"},"references":{"count":48,"sample":[{"doi":"","year":2007,"title":"G\\\" o kova Geom","work_id":"d18e93ff-e5a2-47fc-bea6-50acab42d352","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"Guillem Cazassus, Equivariant Lagrangian Floer homology via cotangent bundles of EG_N , J. 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