On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions
The Abuaf-Ueda flop is a 7-dimensional flop related to ₂ homogeneous spaces. The derived equivalence for this flop was first proved by Ueda using mutations of semi-orthogonal decompositions. In this article, we give an alternative proof of the derived equivalence using tilting bundles. Our proof als...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211305 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions. Wahei Hara. SIGMA 17 (2021), 044, 22 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862614154588717056 |
|---|---|
| author | Hara, Wahei |
| author_facet | Hara, Wahei |
| citation_txt | On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions. Wahei Hara. SIGMA 17 (2021), 044, 22 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The Abuaf-Ueda flop is a 7-dimensional flop related to ₂ homogeneous spaces. The derived equivalence for this flop was first proved by Ueda using mutations of semi-orthogonal decompositions. In this article, we give an alternative proof of the derived equivalence using tilting bundles. Our proof also shows the existence of a non-commutative crepant resolution of the singularity appearing in the flopping contraction. We also give some results on moduli spaces of finite-length modules over this non-commutative crepant resolution.
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| first_indexed | 2026-03-14T08:19:46Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211305 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T08:19:46Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hara, Wahei 2025-12-29T11:06:53Z 2021 On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions. Wahei Hara. SIGMA 17 (2021), 044, 22 pages 1815-0659 2020 Mathematics Subject Classification: 14F05 arXiv:1812.10688 https://nasplib.isofts.kiev.ua/handle/123456789/211305 https://doi.org/10.3842/SIGMA.2021.044 The Abuaf-Ueda flop is a 7-dimensional flop related to ₂ homogeneous spaces. The derived equivalence for this flop was first proved by Ueda using mutations of semi-orthogonal decompositions. In this article, we give an alternative proof of the derived equivalence using tilting bundles. Our proof also shows the existence of a non-commutative crepant resolution of the singularity appearing in the flopping contraction. We also give some results on moduli spaces of finite-length modules over this non-commutative crepant resolution. The author would like to express his sincere gratitude to his supervisor, Professor Yasunari Nagai, and Professor Michel Van den Bergh for their advice and encouragement. The author is grateful to Professor Roland Abuaf for informing him about this interesting op, for careful reading of the first version of this article, and for giving me useful comments. The author would also like to thank Professor Shinnosuke Okawa for pointing out the paper [21], Professors Hajime Kaji and Yuki Hirano for their interest and suggestions, and Professor Michael Wemyss for reading and comments. It is also a pleasure to thank the referees for many helpful comments and suggestions. Part of this work was done during the author's stay at Hasselt University. The author would like to thank Hasselt University for the hospitality and excellent working conditions. This work is supported by Grant-in-Aid for JSPS Research Fellow 17J00857. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions Article published earlier |
| spellingShingle | On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions Hara, Wahei |
| title | On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions |
| title_full | On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions |
| title_fullStr | On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions |
| title_full_unstemmed | On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions |
| title_short | On the Abuaf-Ueda Flop via Non-Commutative Crepant Resolutions |
| title_sort | on the abuaf-ueda flop via non-commutative crepant resolutions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211305 |
| work_keys_str_mv | AT harawahei ontheabuafuedaflopvianoncommutativecrepantresolutions |