Academic Journal
Geometric invariant theory for graded additive groups
| Title: | Geometric invariant theory for graded additive groups |
|---|---|
| Authors: | Yikun Qiao |
| Source: | Journal of Algebra. 683:803-833 |
| Publication Status: | Preprint |
| Publisher Information: | Elsevier BV, 2025. |
| Publication Year: | 2025 |
| Subject Terms: | FOS: Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG) |
| Description: | 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. Journal of Algebra |
| Document Type: | Article |
| Language: | English |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2025.06.038 |
| DOI: | 10.48550/arxiv.2404.04622 |
| Access URL: | http://arxiv.org/abs/2404.04622 |
| Rights: | Elsevier TDM CC BY NC ND |
| Accession Number: | edsair.doi.dedup.....c61ec35c6ee5d6d74465da88c096a3cc |
| Database: | OpenAIRE |
| ISSN: | 00218693 |
|---|---|
| DOI: | 10.1016/j.jalgebra.2025.06.038 |