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 potentia...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2012 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148404 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Examples of Matrix Factorizations from SYZ / Cheol-Hyun Cho, H. Hong, S. Lee // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 21 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860119127482433536 |
|---|---|
| author | Cho, Cheol-Hyun Hong, H. Lee, S. |
| author_facet | Cho, Cheol-Hyun Hong, H. Lee, S. |
| citation_txt | Examples of Matrix Factorizations from SYZ / Cheol-Hyun Cho, H. Hong, S. Lee // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 21 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T17:38:01Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148404 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:38:01Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Cho, Cheol-Hyun Hong, H. Lee, S. 2019-02-18T11:40:42Z 2019-02-18T11:40:42Z 2012 Examples of Matrix Factorizations from SYZ / Cheol-Hyun Cho, H. Hong, S. Lee // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 21 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D37; 53D40; 57R18 DOI: http://dx.doi.org/10.3842/SIGMA.2012.053 https://nasplib.isofts.kiev.ua/handle/123456789/148404 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. This paper is a contribution to the Special Issue “Mirror Symmetry and Related Topics”. The full collection is available at http://www.emis.de/journals/SIGMA/mirror symmetry.html.
 First author thank Naichung Conan Leung, Siu Cheong Lau, Kwok Wai Chan, Yong-Geun Oh for helpful discussions and for sharing their ideas. The work of C.-H. Cho was supported by the National Research Foundation of Korea Grant funded by the Korean Government MEST, Basic Research Promotion Fund (NRF-2011-013-C0004). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Examples of Matrix Factorizations from SYZ Article published earlier |
| spellingShingle | Examples of Matrix Factorizations from SYZ Cho, Cheol-Hyun Hong, H. Lee, S. |
| title | Examples of Matrix Factorizations from SYZ |
| title_full | Examples of Matrix Factorizations from SYZ |
| title_fullStr | Examples of Matrix Factorizations from SYZ |
| title_full_unstemmed | Examples of Matrix Factorizations from SYZ |
| title_short | Examples of Matrix Factorizations from SYZ |
| title_sort | examples of matrix factorizations from syz |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148404 |
| work_keys_str_mv | AT chocheolhyun examplesofmatrixfactorizationsfromsyz AT hongh examplesofmatrixfactorizationsfromsyz AT lees examplesofmatrixfactorizationsfromsyz |