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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2023
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| Accès en ligne: | https://arxiv.org/abs/2312.04239 |
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| _version_ | 1866918354394021888 |
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| author | Chan, Kwokwai Ma, Ziming Nikolas Wen, Hao |
| author_facet | Chan, Kwokwai Ma, Ziming Nikolas Wen, Hao |
| contents | We introduce the notion of a logarithmic Landau-Ginzburg (log LG) model, which is essentially given by equipping the central degenerate fiber of the family of Landau-Ginzburg (LG) models mirror to a projective toric manifold with a natural log structure. We show that the state space of the mirror log LG model is naturally isomorphic to that of the original toric manifold. Following Li-Li-Saito, we give a perturbative construction of primitive forms by studying the deformation theory of such a log LG model, which involves both smoothing of the central degenerate fiber and unfolding of the superpotential. This yields a logarithmic Frobenius manifold structure on the base space of the universal unfolding. The primitive forms and flat coordinates we obtained are computable and closely related to the bulk-deformed Lagrangian Floer superpotential of a projective toric manifold, at least in the semi-Fano case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_04239 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A perturbative construction of primitive forms from log Landau-Ginzburg mirrors of toric manifolds Chan, Kwokwai Ma, Ziming Nikolas Wen, Hao Algebraic Geometry We introduce the notion of a logarithmic Landau-Ginzburg (log LG) model, which is essentially given by equipping the central degenerate fiber of the family of Landau-Ginzburg (LG) models mirror to a projective toric manifold with a natural log structure. We show that the state space of the mirror log LG model is naturally isomorphic to that of the original toric manifold. Following Li-Li-Saito, we give a perturbative construction of primitive forms by studying the deformation theory of such a log LG model, which involves both smoothing of the central degenerate fiber and unfolding of the superpotential. This yields a logarithmic Frobenius manifold structure on the base space of the universal unfolding. The primitive forms and flat coordinates we obtained are computable and closely related to the bulk-deformed Lagrangian Floer superpotential of a projective toric manifold, at least in the semi-Fano case. |
| title | A perturbative construction of primitive forms from log Landau-Ginzburg mirrors of toric manifolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2312.04239 |