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arXiv · 2202.12282

The branched deformations of the special Lagrangian submanifolds

Siqi He
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Abstract

The branched deformations of immersed compact special Lagrangian submanifolds are studied in this paper. If there exists a nondegenerate $\mathbb{Z}_2$ harmonic 1-form over a special Lagrangian submanifold $L$, we construct a family of immersed special Lagrangian submanifolds $\tilde{L}_t$, that are diffeomorphic to a branched covering of $L$ and $\tilde{L}_t$ convergence to $2L$ as current. This answers a question suggested by Donaldson. Combining with the work of Abouzaid and Imagi, we obtain constraints for the existence of nondegenerate $\mathbb{Z}_2$ harmonic 1-forms.

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Siqi He. 2022-02-24. The branched deformations of the special Lagrangian submanifolds. https://arxiv.org/abs/2202.12282

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