Hall Polynomials for Weighted projective lines
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909506613542912 |
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| author | Chen, Jiayi Deng, Bangming Ruan, Shiquan |
| author_facet | Chen, Jiayi Deng, Bangming Ruan, Shiquan |
| contents | This paper deals with the triangle singularity defined by the \linebreak equation $f=X_1^{p_1}+X_2^{p_2}+X_3^{p_3}$ for weight triple $(p_1,p_2,p_3)$, as well as the category of coherent sheaves over the weighted projective line $\mathbb{X}$ defined by $f$. We calculate Hall polynomials associated to extensions bundles, line bundles and torsion sheaves over $\mathbb{X}$. By using derived equivalence, this provides a unified conceptual method for calculating Hall polynomials for representations of tame quivers obtained by Szántó and Szöllősi [J. Pure Appl. Alg. {\bf 228} (2024)]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hall Polynomials for Weighted projective lines Chen, Jiayi Deng, Bangming Ruan, Shiquan Representation Theory Algebraic Geometry 17B37, 16G20, 18G60 This paper deals with the triangle singularity defined by the \linebreak equation $f=X_1^{p_1}+X_2^{p_2}+X_3^{p_3}$ for weight triple $(p_1,p_2,p_3)$, as well as the category of coherent sheaves over the weighted projective line $\mathbb{X}$ defined by $f$. We calculate Hall polynomials associated to extensions bundles, line bundles and torsion sheaves over $\mathbb{X}$. By using derived equivalence, this provides a unified conceptual method for calculating Hall polynomials for representations of tame quivers obtained by Szántó and Szöllősi [J. Pure Appl. Alg. {\bf 228} (2024)]. |
| title | Hall Polynomials for Weighted projective lines |
| topic | Representation Theory Algebraic Geometry 17B37, 16G20, 18G60 |
| url | https://arxiv.org/abs/2502.16543 |