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-fiat Calabi–Yau manifolds and toric Fano manifolds. We also speculate the possible applications of these transformations to other more general settings.
Information
Published: 1 January 2010
First available in Project Euclid: 24 November 2018
zbMATH: 1213.14073
MathSciNet: MR2683205
Digital Object Identifier: 10.2969/aspm/05910001
Subjects:
Primary:
14J32
Secondary:
14J45
,
14N35
Keywords:
holomorphic vector bundle
,
Jacobian ring
,
Lagrangian submanifold
,
Landau–Ginzburg model
,
mirror symmetry
,
quantum cohomology
,
SYZ conjecture
,
SYZ transformation
,
toric Fano manifold
Rights: Copyright © 2010 Mathematical Society of Japan
