Uniqueness in the Local Donaldson–Scaduto Conjecture

Gorapada Bera; Saman Habibi Esfahani; Yang Li

doi:10.1093/imrn/rnaf245

Uniqueness in the Local Donaldson–Scaduto Conjecture

Gorapada Bera
, Saman Habibi Esfahani
, Yang Li

Simons Center for Geometry & Physics

Stony Brook University

Research output: Contribution to journal › Article › peer-review

Abstract

The local Donaldson–Scaduto conjecture predicts the existence and uniqueness of a special Lagrangian pair of pants with three asymptotically cylindrical ends in the Calabi–Yau three-fold X× R², where X is an ALE hyperkähler 4-manifold of A2 type. The existence of this special Lagrangian has previously been proved [7]. In this paper, we prove a uniqueness theorem, showing that no other special Lagrangian pair of pants satisfies this conjecture.

Original language	English
Article number	rnaf245
Journal	International Mathematics Research Notices
Volume	2025
Issue number	16
DOIs	https://doi.org/10.1093/imrn/rnaf245
State	Published - Aug 1 2025

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title = "Uniqueness in the Local Donaldson–Scaduto Conjecture",

abstract = "The local Donaldson–Scaduto conjecture predicts the existence and uniqueness of a special Lagrangian pair of pants with three asymptotically cylindrical ends in the Calabi–Yau three-fold X× R2, where X is an ALE hyperk{\"a}hler 4-manifold of A2 type. The existence of this special Lagrangian has previously been proved [7]. In this paper, we prove a uniqueness theorem, showing that no other special Lagrangian pair of pants satisfies this conjecture.",

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N2 - The local Donaldson–Scaduto conjecture predicts the existence and uniqueness of a special Lagrangian pair of pants with three asymptotically cylindrical ends in the Calabi–Yau three-fold X× R2, where X is an ALE hyperkähler 4-manifold of A2 type. The existence of this special Lagrangian has previously been proved [7]. In this paper, we prove a uniqueness theorem, showing that no other special Lagrangian pair of pants satisfies this conjecture.

AB - The local Donaldson–Scaduto conjecture predicts the existence and uniqueness of a special Lagrangian pair of pants with three asymptotically cylindrical ends in the Calabi–Yau three-fold X× R2, where X is an ALE hyperkähler 4-manifold of A2 type. The existence of this special Lagrangian has previously been proved [7]. In this paper, we prove a uniqueness theorem, showing that no other special Lagrangian pair of pants satisfies this conjecture.

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Uniqueness in the Local Donaldson–Scaduto Conjecture

Abstract

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