Holomorphic disks and GIT quotients

2026/05/17 by Yoosik Kim · 1 voice
Mathematics · #math.SG #math.AG

paper · pdf

Abstract

Let G be a connected compact Lie group and let \mathbbG 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 ⊆ X and those bounded by its quotient L/G in the GIT quotient X \mathbin/\mkern-6mu/ \mathbbG. 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.

Citations

• Equivariant Partially Wrapped Fukaya Categories on Liouville Sectors
• Equivariant Floer homology is isomorphic to reduced Floer homology
• Quantization commutes with reduction again: the quantum GIT conjecture I
• Equivariant Lagrangian correspondence and a conjecture of Teleman
• Equivariant Fukaya categories at singular values
• Disk potential functions for polygon spaces
• Disk potential functions for quadrics
• Construction of Kuranishi structures on the moduli spaces of pseudo holomorphic disks: II
• An open quantum Kirwan map
• Lagrangian fibers of Gelfand--Cetlin systems of SO(n)-type
• Lagrangian fibers of Gelfand-Cetlin systems
• Lie groupoid, deformation of unstable curve, and construction of equivariant Kuranishi charts
• Gauge theory and mirror symmetry
• The moment-weight inequality and the Hilbert-Mumford criterion
• Holomorphic orbidiscs and Lagrangian Floer cohomology of symplectic toric orbifolds
• Moment maps and geometric invariant theory
• Cyclic symmetry and adic convergence in LagrangianFloer theory
• Potential functions via toric degenerations
• Toric degenerations of Gelfand-Cetlin systems and potential functions
• Lagrangian Floer theory on compact toric manifolds II : Bulk deformations
• Lagrangian Floer theory on compact toric manifolds I
• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Notes on GIT and symplectic reduction for bundles and varieties
• Holomorphic disc, spin structures and Floer cohomology of the Clifford torus
• Floer cohomology and disc instantons of Lagrangian torus fibers in Fano toric manifolds
• Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc
• Geometric quantization and multiplicities of group representations
• Reduction of symplectic manifolds with symmetry

Discussions

• Yoosik Kim: Holomorphic disks and GIT quotients https://arxiv.org/abs/2605.17298 https://arxiv.org/pdf/2605.17298 https://arxiv.org/html/2605.17298 [bsky, 0 points, 0 comments]

Related

• Moduli of Open Stable Maps to a Homogeneous Space
• Holomorphic Disks and the Chord Conjecture
• J-holomorphic Disks and Lagrangian Squeezing
• Holomorphic disks with boundary on compact Lagrangian surface
• Existence of pseudo-holomorphic disks via non-archimedean disk potentials