Invariant Rings and Quasiaffine Quotients

Details Invariant Rings and Quasiaffine Quotients Invariant Rings and Quasiaffine Quotients

2000-07-12

arxiv.org/abs/math/0007076v1

Mathematics

Algebraic Geometry

11 pages, LaTeX

Scientific paper

We study Hilbert's fourteenth problem from a geometric point of view. Nagata's celebrated counterexample demonstrates that for an arbitrary group action on a variety the ring of invariant functions need not be isomorphic to the ring of functions of an affine variety. Nevertheless one can prove that such a ring of invariants is always isomorphic to the ring of functions on a quasi-affine variety. Conversely, for a given quasi-affine variety V there exists always an action of the additive group on some affine variety W such that the ring of functions of V is isomorphic to the ring of invariant functions on W. Thus a k-algebra occurs as invariant ring for some group acting on a k-variety iff it occurs as function ring for some quasi-affine k-variety.

Affiliated with

Also associated with

No associations

Rating

Invariant Rings and Quasiaffine Quotients does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Invariant Rings and Quasiaffine Quotients, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Invariant Rings and Quasiaffine Quotients will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-279533