### Abstract

We find matrix factorization corresponding to an anti-diagonal in ℂP^{1}×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 ℂP^{1}×ℂP^{1}, which was predicted by Kapustin and Li from B-model calculations.

Original language | English |
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Article number | 053 |

Journal | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |

Volume | 8 |

DOIs | |

Publication status | Published - 2012 Aug 16 |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Mathematical Physics
- Geometry and Topology

### Cite this

*Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)*,

*8*, [053]. https://doi.org/10.3842/SIGMA.2012.053

}

*Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)*, vol. 8, 053. https://doi.org/10.3842/SIGMA.2012.053

**Examples of matrix factorizations from SYZ.** / Cho, Cheol Hyun; Hong, Hansol; Lee, Sangwook.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Examples of matrix factorizations from SYZ

AU - Cho, Cheol Hyun

AU - Hong, Hansol

AU - Lee, Sangwook

PY - 2012/8/16

Y1 - 2012/8/16

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84865812398&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865812398&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2012.053

DO - 10.3842/SIGMA.2012.053

M3 - Article

AN - SCOPUS:84865812398

VL - 8

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 053

ER -