Homological mirror symmetry of toric Fano surfaces via Morse homotopy

Abstract

Strominger-Yau-Zaslow (SYZ) proposed a way of constructing mirror pairs as pairs of torus fibrations. We apply this SYZ construction to toric Fano surfaces as complex manifolds, and discuss the homological mirror symmetry, where we consider Morse homotopy of the moment polytope instead of the Fukaya category.

v3: 50 pages, 5 figures, Fixed typos. arXiv admin note: text overlap with arXiv:2012.06801 by other authors

References in corpus (1)

• Homological mirror symmetry of $\mathbb{C}{P}^n$ and their products via Morse homotopy

Cited by in corpus (1)

• SYZ mirror of Hirzebruch surface ${\mathbb{F}}_k$ and Morse homotopy