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arXiv · 2603.08384

A remark on monoidal structure and homological mirror symmetry

Tatsuki Kuwagaki
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Abstract

For a symplectic geometry $X$, suppose the (derived) Fukaya category $\mathrm{Fuk}(X)$ of $X$ is equipped with a monoidal structure. Then its Balmer spectrum recovers a mirror $Y$ of $X$ if there exists homological mirror symmetry $\mathrm{Fuk}(X)\cong D^b\mathrm{coh}(Y)$ and the monoidal structure is the mirror of the standard one of $D^b\mathrm{coh}(Y)$. In this short note, we fill one gap of this story in the literature: we show that the monoidal structure determines the homological mirror functor $\mathrm{Fuk}(X)\to D^b\mathrm{coh}(Y)$.

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Tatsuki Kuwagaki. 2026-03-09. A remark on monoidal structure and homological mirror symmetry. https://arxiv.org/abs/2603.08384

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