Homological mirror symmetry for weighted projective spaces and Morse Homotopy

Kontsevich and Soibelman discussed homological mirror symmetry by using the SYZ torus fibrations, where they introduced the weighted version of Fukaya-Oh’s Morse homotopy on the base space of the dual torus fibration in the intermediate step. Futaki and Kajiura applied Kontsevich-Soibelman’s approach to the case when a complex manifold $X$ is a smooth compact toric manifold. There, they introduced the category of weighted Morse homotopy on the moment polytope of toric manifolds, and compared this category to the derived category of coherent sheaves on $X$ instead of the Fukaya category. In this paper, we extend their setting to the case of toric orbifolds, and discuss this version of homological mirror symmetry for weighted projective spaces.