Pseudotoric structures and special Lagrangian torus fibrations on certain flag varieties

Kwokwai Chan; Naichung Conan Leung; Changzheng Li

doi:10.1016/j.geomphys.2019.103489

paper

Pseudotoric structures and special Lagrangian torus fibrations on certain flag varieties

arXiv:1811.09774 · doi:10.1016/j.geomphys.2019.103489

Abstract

We construct pseudotoric structures (à la Tyurin) on the two-step flag variety $F ℓ_{1, n - 1; n}$ , 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.

21 pages; v2: minor corrections and references added