Multi-valued Morse homotopy for the SYZ mirror of the complex projective plane
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910247708262400 |
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| author | Nakanishi, Hayato Suen, Yat-Hin |
| author_facet | Nakanishi, Hayato Suen, Yat-Hin |
| contents | We propose a definition of the category $\mathit{Mo}^{\mathrm{mult}}(P)$ of multi-valued Morse homotopy on $P$ consisting of multi-valued functions associated to Lagrangian multi-sections. We then show that a full subcategory $\mathit{Mo}^{\mathrm{mult}}_{\mathcal{E}}(P)$ of $\mathit{Mo}^{\mathrm{mult}}(P)$ is $A_\infty$-equivalent to a full subcategory $\mathit{DG}_{\mathcal{E}}^{\mathrm{vect}}(\mathbb{C}P^2)$ of the category $\mathit{DG}^{\mathrm{vect}}(\mathbb{C}P^2)$ consisting of holomorphic vector bundles over the complex projective plane $\mathbb{C}P^2$. As an application, we study the mirror description for global sections of the holomorphic tangent bundle over $\mathbb{C}P^2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_23404 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multi-valued Morse homotopy for the SYZ mirror of the complex projective plane Nakanishi, Hayato Suen, Yat-Hin Symplectic Geometry Algebraic Geometry Differential Geometry We propose a definition of the category $\mathit{Mo}^{\mathrm{mult}}(P)$ of multi-valued Morse homotopy on $P$ consisting of multi-valued functions associated to Lagrangian multi-sections. We then show that a full subcategory $\mathit{Mo}^{\mathrm{mult}}_{\mathcal{E}}(P)$ of $\mathit{Mo}^{\mathrm{mult}}(P)$ is $A_\infty$-equivalent to a full subcategory $\mathit{DG}_{\mathcal{E}}^{\mathrm{vect}}(\mathbb{C}P^2)$ of the category $\mathit{DG}^{\mathrm{vect}}(\mathbb{C}P^2)$ consisting of holomorphic vector bundles over the complex projective plane $\mathbb{C}P^2$. As an application, we study the mirror description for global sections of the holomorphic tangent bundle over $\mathbb{C}P^2$. |
| title | Multi-valued Morse homotopy for the SYZ mirror of the complex projective plane |
| topic | Symplectic Geometry Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2605.23404 |