Toric degenerations of Calabi--Yau complete intersections and metric SYZ conjecture
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
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| _version_ | 1866913428530003968 |
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| author | Goto, Keita Yamamoto, Yuto |
| author_facet | Goto, Keita Yamamoto, Yuto |
| contents | We consider a toric degeneration $\mathcal{X}$ of Calabi--Yau complete intersections of Batyrev--Borisov in the Gross--Siebert program. For the toric degeneration $\mathcal{X}$, we study the real Monge--Ampère equation corresponding to the non-archimedean Monge--Ampère equation that yields the non-archimedean Calabi--Yau metric. Our main theorem describes the real Monge--Ampère equation in terms of tropical geometry and proves the metric SYZ conjecture for the toric degeneration $\mathcal{X}$ supposing the existence of its solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_09133 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Toric degenerations of Calabi--Yau complete intersections and metric SYZ conjecture Goto, Keita Yamamoto, Yuto Algebraic Geometry We consider a toric degeneration $\mathcal{X}$ of Calabi--Yau complete intersections of Batyrev--Borisov in the Gross--Siebert program. For the toric degeneration $\mathcal{X}$, we study the real Monge--Ampère equation corresponding to the non-archimedean Monge--Ampère equation that yields the non-archimedean Calabi--Yau metric. Our main theorem describes the real Monge--Ampère equation in terms of tropical geometry and proves the metric SYZ conjecture for the toric degeneration $\mathcal{X}$ supposing the existence of its solution. |
| title | Toric degenerations of Calabi--Yau complete intersections and metric SYZ conjecture |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2407.09133 |