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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2012 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148404 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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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nasplib_isofts_kiev_ua-123456789-148404 |
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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 |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| title |
Examples of Matrix Factorizations from SYZ |
| spellingShingle |
Examples of Matrix Factorizations from SYZ Cho, Cheol-Hyun Hong, H. Lee, S. |
| title_short |
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_sort |
examples of matrix factorizations from syz |
| author |
Cho, Cheol-Hyun Hong, H. Lee, S. |
| author_facet |
Cho, Cheol-Hyun Hong, H. Lee, S. |
| publishDate |
2012 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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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| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148404 |
| 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. |
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