Cluster Configuration Spaces of Finite Type
For each Dynkin diagram , we define a ''cluster configuration space'' ℳ and a partial compactification ℳ˜. For = ₙ₋₃, we have ℳₙ₋₃ = ℳ₀,ₙ, the configuration space of points on ℙ¹, and the partial compactification ℳ˜ₙ₋₃ was studied in this case by Brown. The space M˜ is a smooth...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
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| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211435 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Cluster Configuration Spaces of Finite Type. Nima Arkani-Hamed, Song He and Thomas Lam. SIGMA 17 (2021), 092, 41 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862718012456435712 |
|---|---|
| author | Arkani-Hamed, Nima He, Song Lam, Thomas |
| author_facet | Arkani-Hamed, Nima He, Song Lam, Thomas |
| citation_txt | Cluster Configuration Spaces of Finite Type. Nima Arkani-Hamed, Song He and Thomas Lam. SIGMA 17 (2021), 092, 41 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | For each Dynkin diagram , we define a ''cluster configuration space'' ℳ and a partial compactification ℳ˜. For = ₙ₋₃, we have ℳₙ₋₃ = ℳ₀,ₙ, the configuration space of points on ℙ¹, and the partial compactification ℳ˜ₙ₋₃ was studied in this case by Brown. The space M˜ is a smooth affine algebraic variety with a stratification in bijection with the faces of the Chapoton-Fomin-Zelevinsky generalized associahedron. The regular functions on ℳ˜ are generated by coordinates uγ, in bijection with the cluster variables of type , and the relations are described completely in terms of the compatibility degree function of the cluster algebra. As an application, we define and study cluster algebra analogues of tree-level open string amplitudes.
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| first_indexed | 2026-03-20T18:31:28Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211435 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-20T18:31:28Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Arkani-Hamed, Nima He, Song Lam, Thomas 2026-01-02T08:32:52Z 2021 Cluster Configuration Spaces of Finite Type. Nima Arkani-Hamed, Song He and Thomas Lam. SIGMA 17 (2021), 092, 41 pages 1815-0659 2020 Mathematics Subject Classification: 05E14; 13F60; 14N99; 81T30 arXiv:2005.11419 https://nasplib.isofts.kiev.ua/handle/123456789/211435 https://doi.org/10.3842/SIGMA.2021.092 For each Dynkin diagram , we define a ''cluster configuration space'' ℳ and a partial compactification ℳ˜. For = ₙ₋₃, we have ℳₙ₋₃ = ℳ₀,ₙ, the configuration space of points on ℙ¹, and the partial compactification ℳ˜ₙ₋₃ was studied in this case by Brown. The space M˜ is a smooth affine algebraic variety with a stratification in bijection with the faces of the Chapoton-Fomin-Zelevinsky generalized associahedron. The regular functions on ℳ˜ are generated by coordinates uγ, in bijection with the cluster variables of type , and the relations are described completely in terms of the compatibility degree function of the cluster algebra. As an application, we define and study cluster algebra analogues of tree-level open string amplitudes. We thank Mark Spradlin and Hugh Thomas for many discussions related to this work and for closely related collaborations. We thank the anonymous referees for a number of corrections and helpful suggestions to the exposition. T.L. was supported by NSF DMS-1464693, NSF DMS1953852, and by a von Neumann Fellowship from the Institute for Advanced Study. N.A-H. was supported by DOE grant DE-SC0009988. S.H. was supported in part by the National Natural Science Foundation of China under Grants No. 11935013, 11947301, 12047502, 12047503. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Cluster Configuration Spaces of Finite Type Article published earlier |
| spellingShingle | Cluster Configuration Spaces of Finite Type Arkani-Hamed, Nima He, Song Lam, Thomas |
| title | Cluster Configuration Spaces of Finite Type |
| title_full | Cluster Configuration Spaces of Finite Type |
| title_fullStr | Cluster Configuration Spaces of Finite Type |
| title_full_unstemmed | Cluster Configuration Spaces of Finite Type |
| title_short | Cluster Configuration Spaces of Finite Type |
| title_sort | cluster configuration spaces of finite type |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211435 |
| work_keys_str_mv | AT arkanihamednima clusterconfigurationspacesoffinitetype AT hesong clusterconfigurationspacesoffinitetype AT lamthomas clusterconfigurationspacesoffinitetype |