Examples of matrix factorizations from SYZ

We find matrix factorization corresponding to an anti-diagonal in ℂP¹×ℂP¹, 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 ℂP¹×ℂP¹, which was predicted by Kapustin and Li from B-model calculations.