The Rings of Invariants of Finite Abelian Subgroups of $GL(2, C)$ of Order $\leq 18$
Commun. Korean Math. Soc. 1997 Vol. 12, No. 4, 951-973
J. H. Keum, N. S. Choi Kon-kuk University, Kon-kuk University
Abstract : We classify up to conjugation all finite abelian subgroups of $GL(2,C)$ of order $\leq 18$ and compute the generators and relations of their rings of invariants. In other words, we classify all 2-dimensional quotient singularities by an abelian group of order $ \leq $ 18 and compute the generators and relations of their affine coordinate rings.
Keywords : 2-dimensional quotient singularities, ring of invariants, Groebner basis