Regular semisimple Hessenberg varieties with cohomology rings generated in degree two
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909893424840704 |
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| author | Masuda, Mikiya Sato, Takashi |
| author_facet | Masuda, Mikiya Sato, Takashi |
| contents | A regular semisimple Hessenberg variety $\mathrm{Hess}(S,h)$ is a smooth subvariety of the flag variety determined by a square matrix $S$ with distinct eigenvalues and a Hessenberg function $h$. The cohomology ring $H^*(\mathrm{Hess}(S,h))$ is independent of the choice of $S$ and is not explicitly described except for a few cases. In this paper, we characterize the Hessenberg function $h$ such that $H^*(\mathrm{Hess}(S,h))$ is generated in degree two as a ring. It turns out that such $h$ is what is called a (double) lollipop. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2301_03762 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Regular semisimple Hessenberg varieties with cohomology rings generated in degree two Masuda, Mikiya Sato, Takashi Algebraic Geometry Algebraic Topology Symplectic Geometry 57S12 (Primary), 14M15 (Secondary) A regular semisimple Hessenberg variety $\mathrm{Hess}(S,h)$ is a smooth subvariety of the flag variety determined by a square matrix $S$ with distinct eigenvalues and a Hessenberg function $h$. The cohomology ring $H^*(\mathrm{Hess}(S,h))$ is independent of the choice of $S$ and is not explicitly described except for a few cases. In this paper, we characterize the Hessenberg function $h$ such that $H^*(\mathrm{Hess}(S,h))$ is generated in degree two as a ring. It turns out that such $h$ is what is called a (double) lollipop. |
| title | Regular semisimple Hessenberg varieties with cohomology rings generated in degree two |
| topic | Algebraic Geometry Algebraic Topology Symplectic Geometry 57S12 (Primary), 14M15 (Secondary) |
| url | https://arxiv.org/abs/2301.03762 |