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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.04622 |
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Table of 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.