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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211014 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Walls for -Hilb via Reids Recipe. Ben Wormleighton. SIGMA 16 (2020), 106, 38 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 -Hilb ³ in terms of a marking of exceptional subvarieties of -Hilb ³ 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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| ISSN: | 1815-0659 |