Abstract
Let G be the cyclic group of order n, and suppose F is a field containing a primitive nth root of unity. We consider the ring of invariants F[W] G of a three dimensional representation W of G where G ⊂ SL(W). We describe minimal generators and relations for this ring and prove that the lead terms of the relations are quadratic. These minimal generators for the relations form a Gröbner basis with a surprisingly simple combinatorial structure. We describe the graded Betti numbers for a minimal free resolution of F[W] G . The case where W is any two dimensional representation of G is also handled.
Notes
Communicated by I. Shestakov.