Tilting objects in singularity categories of toric Gorenstein varieties
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866909405805543424 |
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| author | Chen, Xiaojun Liu, Leilei Zeng, Jieheng |
| author_facet | Chen, Xiaojun Liu, Leilei Zeng, Jieheng |
| contents | We study certain toric Gorenstein varieties with isolated singularities which are the quotient spaces of generic unimodular representations by the one-dimensional torus, or by the product of the one-dimensional torus with a finite abelian group. Based on the works of Špenko and Van den Bergh [Invent. Math. 210 (2017), no. 1, 3-67] and Mori and Ueyama [Adv. Math. 297 (2016), 54-92], we show that the singularity categories of these varieties admit tilting objects, and hence are triangle equivalent to the perfect categories of some finite dimensional algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_14161 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Tilting objects in singularity categories of toric Gorenstein varieties Chen, Xiaojun Liu, Leilei Zeng, Jieheng Algebraic Geometry Rings and Algebras Representation Theory We study certain toric Gorenstein varieties with isolated singularities which are the quotient spaces of generic unimodular representations by the one-dimensional torus, or by the product of the one-dimensional torus with a finite abelian group. Based on the works of Špenko and Van den Bergh [Invent. Math. 210 (2017), no. 1, 3-67] and Mori and Ueyama [Adv. Math. 297 (2016), 54-92], we show that the singularity categories of these varieties admit tilting objects, and hence are triangle equivalent to the perfect categories of some finite dimensional algebras. |
| title | Tilting objects in singularity categories of toric Gorenstein varieties |
| topic | Algebraic Geometry Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2106.14161 |