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Examples of Matrix Factorizations from SYZ
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- Фізико-технічні та математичні науки
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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- Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8, випуск за цей рік
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Examples of Matrix Factorizations from SYZ
Інший ID:
2010 Mathematics Subject Classification: 53D37; 53D40; 57R18
DOI: http://dx.doi.org/10.3842/SIGMA.2012.053
DOI: http://dx.doi.org/10.3842/SIGMA.2012.053
Посилання:
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.
Підтримка:
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).
Дата:
2012
Переглядів:
514
Завантажень:
251
Анотація:
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.
