On SYZ mirror transformations

Details On SYZ mirror transformations On SYZ mirror transformations

2008-08-11

arxiv.org/abs/0808.1551v2

"New Developments in Algebraic Geometry, Integrable Systems and Mirror Symmetry", 1-30, Adv. Stud. Pure Math., 59, Math. Soc.

Mathematics

Symplectic Geometry

v2: 22 pages; revised according to the updated version of the preprint arXiv:0801.2830; to appear in Advanced Studies in Pure

Scientific paper

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.

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