Toric degenerations of Calabi--Yau complete intersections and metric SYZ conjecture
Abstract
We consider a toric degeneration X of Calabi--Yau complete intersections of Batyrev--Borisov in the Gross--Siebert program. For the toric degeneration X, we study the real Monge--Amp\`ere equation corresponding to the non-archimedean Monge--Amp\`ere equation that yields the non-archimedean Calabi--Yau metric. Our main theorem describes the real Monge--Amp\`ere equation in terms of tropical geometry and proves the metric SYZ conjecture for the toric degeneration X supposing the existence of its solution.
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