Some faithful algebraic braid twist group actions for 3-fold crepant resolutions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913022076780544 |
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| author | Zheng, Luyu |
| author_facet | Zheng, Luyu |
| contents | Let X(1,3,a) be a crepant resolution of the quotient singularity C^3/G, where G is a diagonal cyclic subgroup of SL(3,\C) acting on C^3 with weights (1,3,a). For each such X(1,3,a), we construct a (Q,W)-configuration of spherical objects in the bounded derived category of coherent sheaves. When a=9, the derived category D(X(1,3,9)) admits a faithful algebraic braid twist group action of type D induced by the associated (Q,W)-configuration. When a=13, the derived category D(X(1,3,13)) admits a faithful algebraic braid twist group action of type E. These two cases illustrate the emergence of type D and type E patterns from specific geometric data, supporting a broader conjectural framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09610 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some faithful algebraic braid twist group actions for 3-fold crepant resolutions Zheng, Luyu Algebraic Geometry Let X(1,3,a) be a crepant resolution of the quotient singularity C^3/G, where G is a diagonal cyclic subgroup of SL(3,\C) acting on C^3 with weights (1,3,a). For each such X(1,3,a), we construct a (Q,W)-configuration of spherical objects in the bounded derived category of coherent sheaves. When a=9, the derived category D(X(1,3,9)) admits a faithful algebraic braid twist group action of type D induced by the associated (Q,W)-configuration. When a=13, the derived category D(X(1,3,13)) admits a faithful algebraic braid twist group action of type E. These two cases illustrate the emergence of type D and type E patterns from specific geometric data, supporting a broader conjectural framework. |
| title | Some faithful algebraic braid twist group actions for 3-fold crepant resolutions |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.09610 |