Generators of Invariant Rings

Hendrikus Derksen, University of Michigan

Abstract. Suppose that G is a group acting by automorphisms on a polynomial ring. Nagata gave an example of a ring whose ring of invariant polynomials is not finitely generated. This example is a counterexample to Hilbert's fourteenth problem. We will discuss algorithms and bounds for rings of invariants. In particular, recently Gregor Kemper and I gave an algorithm to compute invariant rings of reductive groups in positive characteristic. We also have a constructive approach to invariant rings which are not finitely generated.