Non-crossing partitions for exceptional hereditary curves
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918225985404928 |
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| author | Baumeister, Barbara Burban, Igor Neaime, Georges Schwabe, Charly |
| author_facet | Baumeister, Barbara Burban, Igor Neaime, Georges Schwabe, Charly |
| contents | We introduce a new class of reflection groups associated with the canonical bilinear lattices of Lenzing, which we call reflection groups of canonical type. The main result of this work is a categorification of the corresponding poset of non-crossing partitions for any such group, realized via the poset of thick subcategories of the category of coherent sheaves on an exceptional hereditary curve generated by an exceptional sequence. A second principal result, essential for the categorification, is a proof of the transitivity of the Hurwitz action in these reflection groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01729 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-crossing partitions for exceptional hereditary curves Baumeister, Barbara Burban, Igor Neaime, Georges Schwabe, Charly Representation Theory Algebraic Geometry We introduce a new class of reflection groups associated with the canonical bilinear lattices of Lenzing, which we call reflection groups of canonical type. The main result of this work is a categorification of the corresponding poset of non-crossing partitions for any such group, realized via the poset of thick subcategories of the category of coherent sheaves on an exceptional hereditary curve generated by an exceptional sequence. A second principal result, essential for the categorification, is a proof of the transitivity of the Hurwitz action in these reflection groups. |
| title | Non-crossing partitions for exceptional hereditary curves |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2512.01729 |