GIT stability and biquotients of $SU(3)$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915619047211008 |
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| author | Hashimoto, Yoshinori Ishida, Hiroaki Kasuya, Hisashi |
| author_facet | Hashimoto, Yoshinori Ishida, Hiroaki Kasuya, Hisashi |
| contents | We study double-sided actions of $(\mathbb{C}^*)^2$ on $SL(3,\mathbb{C})/U$ and the associated quotients, where $U$ is a maximal unipotent subgroup of $SL(3,\mathbb{C})$. The main results of this paper are a sufficient condition for the double-sided quotient to agree with the quotient in terms of the geometric invariant theory (GIT), and an explicit necessary and sufficient condition for $SL(3,\mathbb{C})/U$ to agree with the $χ$-stable locus in its affine closure. We apply this result to characterize certain complex structures on $SU(3)$ which are not left invariant by means of the GIT quotient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20254 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | GIT stability and biquotients of $SU(3)$ Hashimoto, Yoshinori Ishida, Hiroaki Kasuya, Hisashi Algebraic Geometry Complex Variables 32M05, 22E46, 14L24 We study double-sided actions of $(\mathbb{C}^*)^2$ on $SL(3,\mathbb{C})/U$ and the associated quotients, where $U$ is a maximal unipotent subgroup of $SL(3,\mathbb{C})$. The main results of this paper are a sufficient condition for the double-sided quotient to agree with the quotient in terms of the geometric invariant theory (GIT), and an explicit necessary and sufficient condition for $SL(3,\mathbb{C})/U$ to agree with the $χ$-stable locus in its affine closure. We apply this result to characterize certain complex structures on $SU(3)$ which are not left invariant by means of the GIT quotient. |
| title | GIT stability and biquotients of $SU(3)$ |
| topic | Algebraic Geometry Complex Variables 32M05, 22E46, 14L24 |
| url | https://arxiv.org/abs/2509.20254 |