Pith Number

pith:3PARMS4I

pith:2026:3PARMS4I2W4ZF7KQGMWLKKCSB6

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Holomorphic disks and GIT quotients

Yoosik Kim

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.

arxiv:2605.17298 v1 · 2026-05-17 · math.SG · math.AG

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Claims

C1strongest 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.

C2weakest 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).

C3one 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.

References

48 extracted · 48 resolved · 3 Pith anchors

[1] G\" o kova Geom 2007

[2] Guillem Cazassus, Equivariant Lagrangian Floer homology via cotangent bundles of EG_N , J. Topol. 17 (2024), no. 1, Paper No. e12328, 61 pp 2024

[3] Equivariant Partially Wrapped Fukaya Categories on Liouville Sectors 2025 · arXiv:2512.24382

[4] Cheol-Hyun Cho, Holomorphic discs, spin structures, and Floer cohomology of the Clifford torus. Int. Math. Res. Not. IMRN (2004), No. 35, 1803--1843 2004

[5] Julio Sampietro Christ, Equivariant Floer homology is isomorphic to reduced Floer homology, preprint (2025), arXiv:2505.02647 https://arxiv.org/abs/2505.02647 2025

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:50.889300Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dbc1164b88d5b992fd50332cb528520f9339be32204f97213405c92e00adedf4

Aliases

arxiv: 2605.17298 · arxiv_version: 2605.17298v1 · doi: 10.48550/arxiv.2605.17298 · pith_short_12: 3PARMS4I2W4Z · pith_short_16: 3PARMS4I2W4ZF7KQ · pith_short_8: 3PARMS4I

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3PARMS4I2W4ZF7KQGMWLKKCSB6 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: dbc1164b88d5b992fd50332cb528520f9339be32204f97213405c92e00adedf4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "23ab02cb01bc0a4e48c6585a975f1010c51a093dcb6375f776c14812dab3e16f",
    "cross_cats_sorted": [
      "math.AG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2026-05-17T07:20:14Z",
    "title_canon_sha256": "3b24b09553cfba3be02dfc60f88fff84761a856729175c9e826ce2167664eb27"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17298",
    "kind": "arxiv",
    "version": 1
  }
}