Mathematische Zeitschrift

, Volume 244, Issue 1, pp 163–174

Invariant rings and quasiaffine quotients

  • J. Winkelmann

DOI: 10.1007/s00209-002-0484-9

Cite this article as:
Winkelmann, J. Math. Z. (2003) 244: 163. doi:10.1007/s00209-002-0484-9

Abstract.

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. In this paper we will show that nevertheless it is always isomorphic to the ring of functions on a quasi-affine variety.

Mathematics Subject Classification (2000): 13A50, 14R20, 14L30

Copyright information

© Springer-Verlag Berlin Heidel berg

Authors and Affiliations

  • J. Winkelmann
    • 1
  1. 1.Korea Institute for Advanced Study - KIAS, School of Mathematics, 207-43 Cheongryangri-dong, Dongdaemun-gu, Seoul 130-012, Republic Korea KR