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arXiv · 2407.09133

Toric degenerations of Calabi--Yau complete intersections and metric SYZ conjecture

Keita Goto·Yuto Yamamoto
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Abstract

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.

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Keita Goto, Yuto Yamamoto. 2024-07-12. Toric degenerations of Calabi--Yau complete intersections and metric SYZ conjecture. https://arxiv.org/abs/2407.09133

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