Gorenstein Quotient Singularities in Dimension Three (9780821825679)

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If $G$ is a finite subgroup of $G\!L(3,{\mathbb C})$, 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 $S\!L(3,{\mathbb C})$. In this work, the authors begin with a classification of finite subgroups of $S\!L(3,{\mathbb C})$, 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 $G\!L(3,{\mathbb C})$. 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.


Product details

  • Paperback | 88 pages
  • 184.15 x 260.35 x 6.35mm | 181.44g
  • Providence, United States
  • English
  • 0821825674
  • 9780821825679


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