arXiv 1102.21322011-02math.ACmath.AG

Finite separating sets and quasi-affine quotients

Emilie Dufresne

备注：: I corrected typos and fixed the proof of Lemma 5.3, 11 pages
DOI：: 10.1016/j.jpaa.2012.06.007

英文摘要：

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.

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