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SIGMA, 2012, Volume 8, 053, 24 pages (Mi sigma730)  

This article is cited in 5 scientific papers (total in 5 papers)

Examples of matrix factorizations from SYZ

Cheol-Hyun Cho, Hansol Hong, Sangwook Lee

Department of Mathematics, Research Institute of Mathematics, Seoul National University, 1 Kwanak-ro, Kwanak-gu, Seoul, South Korea

Abstract: 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.

Keywords: matrix factorization, Fukaya category, mirror symmetry, Lagrangian Floer theory.

DOI: https://doi.org/10.3842/SIGMA.2012.053

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Full text: http://emis.mi.ras.ru/.../053
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Bibliographic databases:

ArXiv: 1205.4495
MSC: 53D37; 53D40; 57R18
Received: May 15, 2012; in final form August 12, 2012; Published online August 16, 2012
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Citation: Cheol-Hyun Cho, Hansol Hong, Sangwook Lee, “Examples of matrix factorizations from SYZ”, SIGMA, 8 (2012), 053, 24 pp.

Citation in format AMSBIB
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\by Cheol-Hyun Cho, Hansol Hong, Sangwook Lee
\paper Examples of matrix factorizations from SYZ
\jour SIGMA
\yr 2012
\vol 8
\papernumber 053
\totalpages 24
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\crossref{https://doi.org/10.3842/SIGMA.2012.053}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84865812398}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bringmann, Kathrin; Rolen, Larry; Zwegers, Sander, “On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds”, ROYAL SOCIETY OPEN SCIENCE, 2:11 (2015), 150310  crossref  mathscinet  scopus
    2. Ch.-H. Cho, H. Hong, “Finite group actions on Lagrangian Floer theory”, J. Symplectic Geom., 15:2 (2017), 307–420  crossref  mathscinet  zmath  isi
    3. Ch.-H. Cho, H. Hong, S.-Ch. Lau, “Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for $\mathbb{P}^1_{a,b,c}$”, J. Differ. Geom., 106:1 (2017), 45–126  crossref  mathscinet  zmath  isi
    4. K. Bringmann, J. Kaszian, L. Rolen, “Indefinite theta functions arising in Gromov–Witten theory of elliptic orbifolds”, Camb. J. Math., 6:1 (2018), 25–57  crossref  mathscinet  zmath  isi
    5. Cho Ch.-H., Hong H., Lau S.-Ch., “Localized Mirror Functor Constructed From a Lagrangian Torus”, J. Geom. Phys., 136 (2019), 284–320  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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