Invariants for non-reductive group actions
Gergely B\'erczi, Frances Kirwan
TL;DR
This paper establishes finite generation of invariant algebras for certain non-reductive group actions and provides a geometric method for constructing their GIT quotients.
Contribution
It extends invariant theory to non-reductive groups by proving finite generation and offering a geometric construction of GIT quotients.
Findings
Finite generation of invariant algebras for specific non-reductive group actions.
A geometric construction method for GIT quotients in this context.
New theoretical framework for non-reductive invariant theory.
Abstract
We prove finite generation of the algebras of invariants for a class of linear actions of suitable non-reductive groups on projective and affine varieties, and give a geometric construction for their GIT quotients.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology