Degenerations, fibrations and higher rank Landau-Ginzburg models
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866911348519075840 |
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| author | Doran, Charles F. Kostiuk, Jordan You, Fenglong |
| author_facet | Doran, Charles F. Kostiuk, Jordan You, Fenglong |
| contents | We study semi-stable degenerations of quasi-Fano varieties to unions of two pieces. We conjecture that the higher rank Landau-Ginzburg models mirror to these two pieces can be glued together to lower rank Landau-Ginzburg models which are mirror to the original quasi-Fano varieties. We prove this conjecture by relating their Euler characteristics, generalized functional invariants as well as periods. We also use it to conjecture a relation between the degenerations to the normal cones and the fibrewise compactifications of higher rank Landau-Ginzburg models. Furthermore, we use it to iterate the Doran-Harder-Thompson conjecture and obtain higher codimension Calabi-Yau fibrations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_12891 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Degenerations, fibrations and higher rank Landau-Ginzburg models Doran, Charles F. Kostiuk, Jordan You, Fenglong Algebraic Geometry We study semi-stable degenerations of quasi-Fano varieties to unions of two pieces. We conjecture that the higher rank Landau-Ginzburg models mirror to these two pieces can be glued together to lower rank Landau-Ginzburg models which are mirror to the original quasi-Fano varieties. We prove this conjecture by relating their Euler characteristics, generalized functional invariants as well as periods. We also use it to conjecture a relation between the degenerations to the normal cones and the fibrewise compactifications of higher rank Landau-Ginzburg models. Furthermore, we use it to iterate the Doran-Harder-Thompson conjecture and obtain higher codimension Calabi-Yau fibrations. |
| title | Degenerations, fibrations and higher rank Landau-Ginzburg models |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2112.12891 |