Details:
Title  Resolutions of 2 and 3 dimensional rings of invariants for cyclic groups.  Author(s)  John Harrison, David L. Wehlau  Type  Article in Journal  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.  Keywords  Betti numbers, Cyclic group, Gröbner bases, Invariant theory, Minimal resolutions, Monomial ideals, 13A50, 13D02  ISSN  00927872; 15324125/e 
URL 
http://www.tandfonline.com/doi/abs/10.1080/00927872.2012.695834 
Language  English  Journal  Commun. Algebra  Volume  41  Number  11  Pages  42784289  Publisher  Taylor & Francis, Philadelphia, PA  Year  2013  Edition  0  Translation 
No  Refereed 
No 
