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SIGMA 8 (2012), 053, 24 pages arXiv:1205.4495
https://doi.org/10.3842/SIGMA.2012.053
Contribution to the Special Issue “Mirror Symmetry and Related Topics”
Examples of Matrix Factorizations from SYZ
Cheol-Hyun Cho, Hansol Hong and Sangwook Lee
Department of Mathematics, Research Institute of Mathematics, Seoul National University, 1 Kwanak-ro, Kwanak-gu, Seoul, South Korea
Received May 15, 2012, in final form August 12, 2012; Published online August 16, 2012
Abstract
We find matrix factorization corresponding to an anti-diagonal in ${\mathbb C}P^1 \times {\mathbb C}P^1$, 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 ${\mathbb C}P^1 \times {\mathbb C}P^1$, which was predicted by
Kapustin and Li from B-model calculations.
Key words:
matrix factorization; Fukaya category; mirror symmetry; Lagrangian Floer theory.
pdf (3166 kb)
tex (3289 kb)
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