Examples of Matrix Factorizations from SYZ
Cheol-Hyun Cho, Hansol Hong, Sangwook Lee

TL;DR
This paper constructs matrix factorizations for specific Lagrangian submanifolds in various orbifolds and projective spaces, linking symplectic geometry with algebraic models via Strominger-Yau-Zaslow transformations.
Contribution
It provides explicit matrix factorizations for anti-diagonals and circle fibers in weighted projective lines, extending the SYZ approach to orbifolds and confirming predictions from B-model calculations.
Findings
Matrix factorizations for anti-diagonals in ${ m CP}^1 imes { m CP}^1$
Matrix factorizations for circle fibers in weighted projective lines
Equivalence of certain Lagrangian sums with torus fibers in Fukaya category
Abstract
We find matrix factorization corresponding to an anti-diagonal in , 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 and in the Fukaya category of , which was predicted by Kapustin and Li from B-model calculations.
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