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arXiv · 2510.12735

Generic special Lagrangian moduli spaces of a non-Kähler Calabi--Yau threefold

Benjamin Friedman
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Abstract

Given a (possibly non-Kähler) Calabi--Yau threefold $(X,Ω)$, we introduce the notion of a (perturbed) special Lagrangian (SL) submanifold of $(X,ω,Ω)$, where $ω$ is a Hermitian metric on $X$. The equations defining this class of submanifolds reduce to the usual SL equations when $ω$ is a Kähler metric. Using the Sard--Smale technique, we prove the existence of a comeagre set of Hermitian metrics $ω$ on $X$ such that the moduli space of perturbed SL submanifolds in $(X,ω,Ω)$ consists of isolated points.

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Benjamin Friedman. 2025-10-14. Generic special Lagrangian moduli spaces of a non-Kähler Calabi--Yau threefold. https://arxiv.org/abs/2510.12735

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