New Titles  |  FAQ  |  Keep Informed  |  Review Cart  |  Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education
Gorenstein Quotient Singularities in Dimension Three
 SEARCH THIS BOOK:
Memoirs of the American Mathematical Society
1993; 88 pp; softcover
Volume: 105
ISBN-10: 0-8218-2567-4
ISBN-13: 978-0-8218-2567-9
List Price: US$34 Individual Members: US$20.40
Institutional Members: US\$27.20
Order Code: MEMO/105/505

If $$G$$ is a finite subgroup of $$GL(3,{\mathbb C})$$, then $$G$$ acts on $${\mathbb C}^3$$, and it is known that $${\mathbb C}^3/G$$ is Gorenstein if and only if $$G$$ is a subgroup of $$SL(3,{\mathbb C})$$. In this work, the authors begin with a classification of finite subgroups of $$SL(3,{\mathbb C})$$, including two types, (J) and (K), which have often been overlooked. They go on to present a general method for finding invariant polynomials and their relations to finite subgroups of $$GL(3,{\mathbb C})$$. The method is, in practice, substantially better than the classical method due to Noether. Some properties of quotient varieties are presented, along with a proof that $${\mathbb C}^3/G$$ has isolated singularities if and only if $$G$$ is abelian and 1 is not an eigenvalue of $$g$$ for every nontrivial $$g \in G$$. The authors also find minimal quotient generators of the ring of invariant polynomials and relations among them.

• Classification of finite subgroups of $$SL(3,\mathbb C)$$
• The invariant polynomials and their relations of linear groups of $$SL(3,\mathbb C)$$