A recollement approach to Brieskorn-Pham singularities
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914192675569664 |
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| author | Weng, Weikang |
| author_facet | Weng, Weikang |
| contents | In this paper, we construct recollements and ladders for Brieskorn-Pham singularities via reduction/insertion functors, and study the singularity categories of the Brieskorn-Pham singularities using these ladders.
In particular, we construct a class of tilting objects, called the extended tilting $n$-cuboids, whose endomorphism algebras are $n$-fold tensor products of certain Nakayama algebras. Moreover, we show that such an endomorphism algebra is derived equivalent to a certain replicated algebra. This generalizes the Happel-Seidel symmetry to the context of Brieskorn-Pham singularities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09692 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A recollement approach to Brieskorn-Pham singularities Weng, Weikang Representation Theory Algebraic Geometry In this paper, we construct recollements and ladders for Brieskorn-Pham singularities via reduction/insertion functors, and study the singularity categories of the Brieskorn-Pham singularities using these ladders. In particular, we construct a class of tilting objects, called the extended tilting $n$-cuboids, whose endomorphism algebras are $n$-fold tensor products of certain Nakayama algebras. Moreover, we show that such an endomorphism algebra is derived equivalent to a certain replicated algebra. This generalizes the Happel-Seidel symmetry to the context of Brieskorn-Pham singularities. |
| title | A recollement approach to Brieskorn-Pham singularities |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2512.09692 |