Modularity of Landau-Ginzburg models
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916970908090368 |
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| author | Doran, Charles Harder, Andrew Katzarkov, Ludmil Ovcharenko, Mikhail Przyjalkowski, Victor |
| author_facet | Doran, Charles Harder, Andrew Katzarkov, Ludmil Ovcharenko, Mikhail Przyjalkowski, Victor |
| contents | For each Fano threefold, we construct a family of Landau-Ginzburg models which satisfy many expectations coming from different aspects of mirror symmetry; they are log Calabi-Yau varieties with proper potential maps; they admit open algebraic torus charts on which the potential function $w$ restricts to a Laurent polynomial satisfying a deformation of the Minkowski ansatz; the general fibres of $w$ are Dolgachev-Nikulin dual to the anticanonical hypersurfaces in $X$. To do this, we study the deformation theory of Landau-Ginzburg models in arbitrary dimension, following the third-named author, Kontsevich, and Pantev, specializing to the case of Landau-Ginzburg models obtained from Laurent polynomials. Our proof of Dolgachev-Nikulin mirror symmetry is by detailed case-by-case analysis, refining work of Cheltsov and the fifth-named author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_15607 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Modularity of Landau-Ginzburg models Doran, Charles Harder, Andrew Katzarkov, Ludmil Ovcharenko, Mikhail Przyjalkowski, Victor Algebraic Geometry 14J45, 14J32 For each Fano threefold, we construct a family of Landau-Ginzburg models which satisfy many expectations coming from different aspects of mirror symmetry; they are log Calabi-Yau varieties with proper potential maps; they admit open algebraic torus charts on which the potential function $w$ restricts to a Laurent polynomial satisfying a deformation of the Minkowski ansatz; the general fibres of $w$ are Dolgachev-Nikulin dual to the anticanonical hypersurfaces in $X$. To do this, we study the deformation theory of Landau-Ginzburg models in arbitrary dimension, following the third-named author, Kontsevich, and Pantev, specializing to the case of Landau-Ginzburg models obtained from Laurent polynomials. Our proof of Dolgachev-Nikulin mirror symmetry is by detailed case-by-case analysis, refining work of Cheltsov and the fifth-named author. |
| title | Modularity of Landau-Ginzburg models |
| topic | Algebraic Geometry 14J45, 14J32 |
| url | https://arxiv.org/abs/2307.15607 |