Academic Journal

Geometric invariant theory for graded additive groups

Bibliographic Details
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
Description
ISSN:00218693
DOI:10.1016/j.jalgebra.2025.06.038