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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2017 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2017
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148604 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862544262670843904 |
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| author | Kanazawa, A. |
| author_facet | Kanazawa, A. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-25T01:48:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148604 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T01:48:45Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kanazawa, A. 2019-02-18T16:29:46Z 2019-02-18T16:29:46Z 2017 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 https://nasplib.isofts.kiev.ua/handle/123456789/148604 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. The author would like to thank Yu-Wei Fan, Andrew Harder, Hansol Hong and Siu-Cheong Lau
 for useful conversations on related topics. Special thanks go to the referees for their valuable
 comments and improvements to this article. This research was supported by the Kyoto University Hakubi Project. Part of this work was carried out during the author’s stay at BIRS in the
 fall of 2016. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves Article published earlier |
| spellingShingle | Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves Kanazawa, A. |
| title | 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_short | Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves |
| title_sort | doran-harder-thompson conjecture via syz mirror symmetry: elliptic curves |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148604 |
| work_keys_str_mv | AT kanazawaa doranharderthompsonconjectureviasyzmirrorsymmetryellipticcurves |