Finite separating sets and quasi-affine quotients

Emilie Dufresne*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Nagata's famous counterexample to Hilbert's fourteenth problem shows that the ring of invariants of an algebraic group action on an affine algebraic variety is not always finitely generated. In some sense, however, invariant rings are not far from affine. Indeed, invariant rings are always quasi-affine, and there always exist finite separating sets. In this paper, we give a new method for finding a quasi-affine variety on which the ring of regular functions is equal to a given invariant ring, and we give a criterion to recognize separating algebras. The method and criterion are used on some known examples and in a new construction.

Original languageEnglish
Pages (from-to)247-253
Number of pages7
JournalJournal of Pure and Applied Algebra
Volume217
Issue number2
DOIs
Publication statusPublished - 1 Feb 2013

Cite this