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

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.

12 pages. arXiv admin note: text overlap with arXiv:2404.04972