Generic special Lagrangian moduli spaces of a non-Kähler Calabi--Yau threefold
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912647057768448 |
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| author | Friedman, Benjamin |
| author_facet | Friedman, Benjamin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_12735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generic special Lagrangian moduli spaces of a non-Kähler Calabi--Yau threefold Friedman, Benjamin Differential Geometry 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. |
| title | Generic special Lagrangian moduli spaces of a non-Kähler Calabi--Yau threefold |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2510.12735 |