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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.18618 |
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| _version_ | 1866915463293829120 |
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| author | Chen, Jianmin Zheng, Yiting |
| author_facet | Chen, Jianmin Zheng, Yiting |
| contents | We provide a combinatorial description of morphisms in the coherent sheaf category ${\rm coh}\mbox{-}\mathbb{X}(p,q)$ over weighted projective line of type $(p,q)$ via a marked annulus. This leads to a geometric realization of exceptional sequences in ${\rm coh}\mbox{-}\mathbb{X}(p,q)$. As applications, we present a classification of complete exceptional sequences, an effective method for enlarging exceptional sequences, and a new proof of the transitivity of the braid group action on complete exceptional sequences. Besides, we offer a combinatorial description of tilting bundles via lattice paths and count the number of tilting sheaves in ${\rm coh}\mbox{-}\mathbb{X}(p,q)$, up to the Auslander-Reiten translation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_18618 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Combinatorial Approaches to Exceptional Sequences for Weighted Projective Lines of Type $(p,q)$ Chen, Jianmin Zheng, Yiting Representation Theory Combinatorics We provide a combinatorial description of morphisms in the coherent sheaf category ${\rm coh}\mbox{-}\mathbb{X}(p,q)$ over weighted projective line of type $(p,q)$ via a marked annulus. This leads to a geometric realization of exceptional sequences in ${\rm coh}\mbox{-}\mathbb{X}(p,q)$. As applications, we present a classification of complete exceptional sequences, an effective method for enlarging exceptional sequences, and a new proof of the transitivity of the braid group action on complete exceptional sequences. Besides, we offer a combinatorial description of tilting bundles via lattice paths and count the number of tilting sheaves in ${\rm coh}\mbox{-}\mathbb{X}(p,q)$, up to the Auslander-Reiten translation. |
| title | Combinatorial Approaches to Exceptional Sequences for Weighted Projective Lines of Type $(p,q)$ |
| topic | Representation Theory Combinatorics |
| url | https://arxiv.org/abs/2508.18618 |