Survey on the metric SYZ conjecture and non-archimedean geometry

Abstract

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.

48 pages. arXiv admin note: text overlap with arXiv:2007.01384

References in corpus (3)

• Conjectures on Bridgeland stability for Fukaya categories of Calabi-Yau manifolds, special Lagrangians, and Lagrangian mean curvature flow
• The non-archimedean SYZ fibration
• An extension theorem for Kähler currents