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Survey on the metric SYZ conjecture and non-archimedean geometry

We survey the metric aspects of the Strominger-Yau-Zaslow conjecture on the existence of special Lagrangian fibrations on Calabi-Yau manifolds near the large complex structure limit. We will discuss the diverse motivations for the conjectural picture, what the best hopes are, and a number of subtleties. The bulk of the survey highlights the role of pluripotential theory, and non-archimedean geometry in particular, with a list of open questions.

preprint2022arXivOpen access
Yang Li
math.AGmath.DG
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Yang Li

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