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SPECIAL LAGRANGIAN FIBRATIONS, WALL-CROSSING, AND MIRROR SYMMETRY
 

Summary: SPECIAL LAGRANGIAN FIBRATIONS, WALL-CROSSING, AND
MIRROR SYMMETRY
DENIS AUROUX
Abstract. In this survey paper, we briefly review various aspects of the SYZ
approach to mirror symmetry for non-Calabi-Yau varieties, focusing in particular
on Lagrangian fibrations and wall-crossing phenomena in Floer homology. Various
examples are presented, some of them new.
Contents
1. Introduction 2
2. Lagrangian tori and mirror symmetry 3
2.1. Lagrangian tori and the SYZ conjecture 3
2.2. Beyond the Calabi-Yau case: Landau-Ginzburg models 6
2.3. Example: Fano toric varieties 10
3. Examples of wall-crossing and instanton corrections 12
3.1. First examples 12
3.2. Beyond the Fano case: Hirzebruch surfaces 16
3.3. Higher dimensions 23
4. Floer-theoretic considerations 29
4.1. Deformations and local systems 29
4.2. Failure of invariance and divergence issues 33

  

Source: Auroux, Denis - Department of Mathematics, Massachusetts Institute of Technology (MIT)

 

Collections: Mathematics