English

On SYZ mirror transformations

Symplectic Geometry 2010-10-25 v2 Algebraic Geometry

Abstract

In this expository paper, we discuss how Fourier-Mukai-type transformations, which we call SYZ mirror transformations, can be applied to provide a geometric understanding of the mirror symmetry phenomena for semi-flat Calabi-Yau manifolds and toric Fano manifolds. We also speculate the possible applications of these transformations to other more general settings.

Keywords

Cite

@article{arxiv.0808.1551,
  title  = {On SYZ mirror transformations},
  author = {Kwokwai Chan and Naichung Conan Leung},
  journal= {arXiv preprint arXiv:0808.1551},
  year   = {2010}
}

Comments

v2: 22 pages; revised according to the updated version of the preprint arXiv:0801.2830; to appear in Advanced Studies in Pure Mathematics, "New Developments in Algebraic Geometry, Integrable Systems and Mirror Symmetry"

R2 v1 2026-06-21T11:09:27.060Z