English

Survey on the metric SYZ conjecture and non-archimedean geometry

Algebraic Geometry 2022-09-07 v1 Differential 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.

Keywords

Cite

@article{arxiv.2204.11363,
  title  = {Survey on the metric SYZ conjecture and non-archimedean geometry},
  author = {Yang Li},
  journal= {arXiv preprint arXiv:2204.11363},
  year   = {2022}
}

Comments

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