Geometric invariant theory for graded additive groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908452086874112 |
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| author | Qiao, Yikun |
| author_facet | Qiao, Yikun |
| contents | We consider geometric invariant theory for \emph{graded additive groups}, groups of the form $\mathbb{G}_a^r\rtimes_w\mathbb{G}_m$ such that the $\mathbb{G}_m$-action on $\mathbb{G}_a^r$ is a scalar multiplication with weight $w\in\mathbb{N}_+$. We provide an algorithm of equivariant birational modifications, such that we can apply the geometric invariant theory of Bérczi-Doran-Hawes-Kirwan. In particular, the geometric $\mathbb{G}_a^r$-quotient exists. This complements Bérczi-Doran-Hawes-Kirwan, in the special case of one grading weight. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04622 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric invariant theory for graded additive groups Qiao, Yikun Algebraic Geometry We consider geometric invariant theory for \emph{graded additive groups}, groups of the form $\mathbb{G}_a^r\rtimes_w\mathbb{G}_m$ such that the $\mathbb{G}_m$-action on $\mathbb{G}_a^r$ is a scalar multiplication with weight $w\in\mathbb{N}_+$. We provide an algorithm of equivariant birational modifications, such that we can apply the geometric invariant theory of Bérczi-Doran-Hawes-Kirwan. In particular, the geometric $\mathbb{G}_a^r$-quotient exists. This complements Bérczi-Doran-Hawes-Kirwan, in the special case of one grading weight. |
| title | Geometric invariant theory for graded additive groups |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2404.04622 |