Invariant Rings and Quasiaffine Quotients

dc.creatorWinkelmann, Joerg
dc.date2000-07-12
dc.date.accessioned2026-07-07T04:36:21Z
dc.date.available2026-07-07T04:36:21Z
dc.descriptionWe 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.
dc.description11 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/0007076
dc.identifierhttp://arxiv.org/abs/math/0007076
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/59564
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subject13A50, 14R20, 14L30
dc.titleInvariant Rings and Quasiaffine Quotients
dc.typetext

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