Walls for -Hilb via Reids Recipe
The three-dimensional McKay correspondence seeks to relate the geometry of crepant resolutions of Gorenstein 3-fold quotient singularities ³/ with the representation theory of the group . The first crepant resolution studied in depth was the -Hilbert scheme -HilbA3, which is also a moduli space of θ...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211014 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Walls for -Hilb via Reids Recipe. Ben Wormleighton. SIGMA 16 (2020), 106, 38 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862632768094076928 |
|---|---|
| author | Wormleighton, Ben |
| author_facet | Wormleighton, Ben |
| citation_txt | Walls for -Hilb via Reids Recipe. Ben Wormleighton. SIGMA 16 (2020), 106, 38 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The three-dimensional McKay correspondence seeks to relate the geometry of crepant resolutions of Gorenstein 3-fold quotient singularities ³/ with the representation theory of the group . The first crepant resolution studied in depth was the -Hilbert scheme -HilbA3, which is also a moduli space of θ-stable representations of the McKay quiver associated to . As the stability parameter θ varies, we obtain many other crepant resolutions. In this paper, we focus on the case where is abelian, and compute explicit inequalities for the chamber of the stability space defining -Hilb³ in terms of a marking of exceptional subvarieties of -Hilb³ called Reid's recipe. We further show which of these inequalities define walls. This procedure depends only on the combinatorics of the exceptional fibre and has applications to the birational geometry of other crepant resolutions.
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| first_indexed | 2026-03-14T20:34:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211014 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-14T20:34:07Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Wormleighton, Ben 2025-12-22T09:28:46Z 2020 Walls for -Hilb via Reids Recipe. Ben Wormleighton. SIGMA 16 (2020), 106, 38 pages 1815-0659 2020 Mathematics Subject Classification: 14E16; 14M25; 16G20 arXiv:1908.05748 https://nasplib.isofts.kiev.ua/handle/123456789/211014 https://doi.org/10.3842/SIGMA.2020.106 The three-dimensional McKay correspondence seeks to relate the geometry of crepant resolutions of Gorenstein 3-fold quotient singularities ³/ with the representation theory of the group . The first crepant resolution studied in depth was the -Hilbert scheme -HilbA3, which is also a moduli space of θ-stable representations of the McKay quiver associated to . As the stability parameter θ varies, we obtain many other crepant resolutions. In this paper, we focus on the case where is abelian, and compute explicit inequalities for the chamber of the stability space defining -Hilb³ in terms of a marking of exceptional subvarieties of -Hilb³ called Reid's recipe. We further show which of these inequalities define walls. This procedure depends only on the combinatorics of the exceptional fibre and has applications to the birational geometry of other crepant resolutions. The author would like to thank Yukari Ito and Nagoya University for hosting him as this research began. He would also like to thank Alastair Craw, Alvaro Nolla de Celis, and David Nadler for many fruitful and enjoyable conversations about this project, as well as the referees for their thoughtful suggestions on how to improve its exposition. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Walls for -Hilb via Reids Recipe Article published earlier |
| spellingShingle | Walls for -Hilb via Reids Recipe Wormleighton, Ben |
| title | Walls for -Hilb via Reids Recipe |
| title_full | Walls for -Hilb via Reids Recipe |
| title_fullStr | Walls for -Hilb via Reids Recipe |
| title_full_unstemmed | Walls for -Hilb via Reids Recipe |
| title_short | Walls for -Hilb via Reids Recipe |
| title_sort | walls for -hilb via reids recipe |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211014 |
| work_keys_str_mv | AT wormleightonben wallsforhilbviareidsrecipe |