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Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves
We prove the Doran-Harder-Thompson conjecture in the case of elliptic curves by using ideas from SYZ mirror symmetry. The conjecture claims that when a Calabi-Yau manifold X degenerates to a union of two quasi-Fano manifolds (Tyurin degeneration), a mirror Calabi-Yau manifold of X can be constructed...
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Інститут математики НАН України
2017
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/148604 |
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irk-123456789-1486042019-02-19T01:29:07Z Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves Kanazawa, A. We prove the Doran-Harder-Thompson conjecture in the case of elliptic curves by using ideas from SYZ mirror symmetry. The conjecture claims that when a Calabi-Yau manifold X degenerates to a union of two quasi-Fano manifolds (Tyurin degeneration), a mirror Calabi-Yau manifold of X can be constructed by gluing the two mirror Landau-Ginzburg models of the quasi-Fano manifolds. The two crucial ideas in our proof are to obtain a complex structure by gluing the underlying affine manifolds and to construct the theta functions from the Landau-Ginzburg superpotentials. 2017 Article Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves / A. Kanazawa // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 21 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 53D37; 14J33; 14J32; 14J45; 14D06 DOI:10.3842/SIGMA.2017.024 http://dspace.nbuv.gov.ua/handle/123456789/148604 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
We prove the Doran-Harder-Thompson conjecture in the case of elliptic curves by using ideas from SYZ mirror symmetry. The conjecture claims that when a Calabi-Yau manifold X degenerates to a union of two quasi-Fano manifolds (Tyurin degeneration), a mirror Calabi-Yau manifold of X can be constructed by gluing the two mirror Landau-Ginzburg models of the quasi-Fano manifolds. The two crucial ideas in our proof are to obtain a complex structure by gluing the underlying affine manifolds and to construct the theta functions from the Landau-Ginzburg superpotentials. |
| format |
Article |
| author |
Kanazawa, A. |
| spellingShingle |
Kanazawa, A. Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Kanazawa, A. |
| author_sort |
Kanazawa, A. |
| title |
Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves |
| title_short |
Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves |
| title_full |
Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves |
| title_fullStr |
Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves |
| title_full_unstemmed |
Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves |
| title_sort |
doran-harder-thompson conjecture via syz mirror symmetry: elliptic curves |
| publisher |
Інститут математики НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148604 |
| citation_txt |
Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves / A. Kanazawa // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 21 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT kanazawaa doranharderthompsonconjectureviasyzmirrorsymmetryellipticcurves |
| first_indexed |
2023-05-20T17:30:13Z |
| last_indexed |
2023-05-20T17:30:13Z |
| _version_ |
1796153441272201216 |