Gorenstein Quotient Singularities in Dimension Three

ISBN-13: 9780821825679 / Angielski / Miękka / 1993 / 88 str.

Opis

If $G$ is a finite subgroup of $GL(3, {Bbb C )$, then $G$ acts on ${Bbb C $, and it is known that ${Bbb C /G$ is Gorenstein if and only if $G$ is a subgroup of $SL(3, {Bbb C )$. In this work, the authors begin with a classification of finite subgroups of $SL(3, {Bbb C )$, inlcuding 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 $GL(3, {Bbb C )$. 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 ${Bbb C /G$ 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 t