Affine Non-Reductive GIT and moduli of representations of quivers with multiplicities

2024/04/09 by Eloise Hamilton, Victoria Hoskins, Hamilton, Eloise +3 · 1 citation
Mathematics · Physics and Astronomy · #14D20 (Secondary) #14L24 and 16G20 (Primary) #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2404.06560

openalex publication_date 2024/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an explicit approach to quotienting affine varieties by linear actions of linear algebraic groups with graded unipotent radical, using results from projective Non-Reductive GIT. Our quotients come with explicit projective completions, whose boundaries we interpret in terms of the original action. As an application we construct moduli spaces of semistable representations of quivers with multiplicities subject to certain conditions, which always hold in the toric case for a generic stability condition.

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• Moduli spaces for Θ-strata and non-reductive quotients

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