Dominic Bunnett › The non-reductive zoo
The non-reductive zoo
A collection of examples and curious phenomena in non-reductive group actions and invariant theory.
The cages below are examples I have had lying around for a while. I write each one up in LaTeX, and an AI tool turns the file into a Quarto page and adds it to the zoo.
If you have an example that deserves to be housed here, please email me at bunnett at math.tu-berlin.de.
- Nagata’s counterexample to finite generation How Nagata’s theorem on plane curves produces a linear representation of a vector group whose invariant ring is not finitely generated.
- Roberts’ counterexample to finite generation A nonlinear additive-group action on affine seven-space with a non-finitely generated invariant ring.
- Two closed orbits in one orbit closure A linear action of the Borel subgroup of SL(2) on its Lie algebra with an orbit closure containing two closed orbits.
No matching items