English

Recent progress on SYZ mirror symmetry for some non-compact Calabi-Yau surfaces

Differential Geometry 2022-09-01 v1 Algebraic Geometry

Abstract

We survey the authors recent works, joint with A. Jacob, on Strominger-Yau-Zaslow mirror symmetry for rational elliptic surfaces and del Pezzo surfaces. We discuss some applications, including the Torelli theorem for ALHALH^* gravitational instantons and explain how our results can be used to prove that all ALHALH^* gravitational instantons can be compactified to a weak del Pezzo surface, recovering a recent result of Hein-Sun-Viaclovsky-Zhang.

Keywords

Cite

@article{arxiv.2208.14485,
  title  = {Recent progress on SYZ mirror symmetry for some non-compact Calabi-Yau surfaces},
  author = {Tristan C. Collins and Yu-Shen Lin},
  journal= {arXiv preprint arXiv:2208.14485},
  year   = {2022}
}

Comments

survey article; 29 pages