ACM tilting bundles on a Geigle-Lenzing projective plane of type $(2,2,2,p)$
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| Format: | Preprint |
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2025
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| _version_ | 1866916795712012288 |
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| author | Chen, Jianmin Ruan, Shiquan Weng, Weikang |
| author_facet | Chen, Jianmin Ruan, Shiquan Weng, Weikang |
| contents | Let $\mathbb{X}$ be a Geigle-Lenzing projective plane of type $(2,2,2,p)$ and $\mathsf{coh} \mathbb{X}$ the category of coherent sheaves on $\mathbb{X}$. This paper is devoted to study ACM tilting bundles over $\mathbb{X}$, that is, tilting objects in the derived category $\mathsf{D}^{\rm b}(\mathsf{coh} \, \mathbb{X})$ that are also ACM bundles. We show that a tilting bundle consisting of line bundles is the $2$-canonical tilting bundle up to degree shift. We also provide a program to construct ACM tilting bundles, which give a rich source of (almost) $2$-representation infinite algebras. As an application, we give a classification result of ACM tilting bundles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13376 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | ACM tilting bundles on a Geigle-Lenzing projective plane of type $(2,2,2,p)$ Chen, Jianmin Ruan, Shiquan Weng, Weikang Representation Theory Algebraic Geometry Let $\mathbb{X}$ be a Geigle-Lenzing projective plane of type $(2,2,2,p)$ and $\mathsf{coh} \mathbb{X}$ the category of coherent sheaves on $\mathbb{X}$. This paper is devoted to study ACM tilting bundles over $\mathbb{X}$, that is, tilting objects in the derived category $\mathsf{D}^{\rm b}(\mathsf{coh} \, \mathbb{X})$ that are also ACM bundles. We show that a tilting bundle consisting of line bundles is the $2$-canonical tilting bundle up to degree shift. We also provide a program to construct ACM tilting bundles, which give a rich source of (almost) $2$-representation infinite algebras. As an application, we give a classification result of ACM tilting bundles. |
| title | ACM tilting bundles on a Geigle-Lenzing projective plane of type $(2,2,2,p)$ |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2506.13376 |