Pseudotoric structures and special Lagrangian torus fibrations on certain flag varieties

Abstract

We construct pseudotoric structures (à la Tyurin) on the two-step flag variety $F{\ell }_{1,n-1;n}$, and explain a general relation between pseudotoric structures and special Lagrangian torus fibrations, the latter of which are important in the study of SYZ mirror symmetry. As an application, we speculate how our constructions can explain the number of terms in the superpotential of Rietsch's Landau-Ginzburg mirror.

arXiv comment21 pages; v2: minor corrections and references added

References in corpus (7)

• Mirror Symmetry is T-Duality
• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• SYZ mirror symmetry for toric Calabi-Yau manifolds
• Lagrangian torus fibrations and homological mirror symmetry for the conifold
• Immersed two-spheres and SYZ with Application to Grassmannians
• Potential functions via toric degenerations
• Potential functions on Grassmannians of planes and cluster transformations