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arXiv · 2605.17298

Holomorphic disks and GIT quotients

Yoosik Kim
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Abstract

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.

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Yoosik Kim. 2026-05-17. Holomorphic disks and GIT quotients. https://arxiv.org/abs/2605.17298

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