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arXiv · 2510.12735

Generic special Lagrangian moduli spaces of a non-K\"ahler Calabi--Yau threefold

Benjamin Friedman
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Abstract

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

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

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