A remark on monoidal structure and homological mirror symmetry
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918380008636416 |
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| author | Kuwagaki, Tatsuki |
| author_facet | Kuwagaki, Tatsuki |
| contents | 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 $\mathrm{Fuk}(X)\to D^b\mathrm{coh}(Y)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_08384 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A remark on monoidal structure and homological mirror symmetry Kuwagaki, Tatsuki Symplectic Geometry Algebraic Geometry 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 $\mathrm{Fuk}(X)\to D^b\mathrm{coh}(Y)$. |
| title | A remark on monoidal structure and homological mirror symmetry |
| topic | Symplectic Geometry Algebraic Geometry |
| url | https://arxiv.org/abs/2603.08384 |