Examples of matrix factorizations from SYZ

We find matrix factorization corresponding to an anti-diagonal in $\mathbb CP^1 \times \mathbb CP^1$, and circle fibers in weighted projective lines using the idea of Chan and Leung of Strominger–Yau–Zaslow transformations. For the tear drop orbifolds, we apply this idea to find matrix factorizations for two types of potential, the usual Hori–Vafa potential or the bulk deformed (orbi)-potential. We also show that the direct sum of anti-diagonal with its shift, is equivalent to the direct sum of central torus fibers with holonomy $(1,-1)$ and $(-1,1)$ in the Fukaya category of $\mathbb CP^1 \times \mathbb CP^1$, which was predicted by Kapustin and Li from B-model calculations.