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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","authors_text":"Yoosik Kim","cross_cats":["math.AG"],"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.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.SG","submitted_at":"2026-05-17T07:20:14Z","title":"Holomorphic disks and GIT quotients"},"references":{"count":48,"internal_anchors":3,"resolved_work":48,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"G\\\" o kova Geom","work_id":"d18e93ff-e5a2-47fc-bea6-50acab42d352","year":2007},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Guillem Cazassus, Equivariant Lagrangian Floer homology via cotangent bundles of EG_N , J. 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