Gorenstein quotient singularities in dimension three
Author(s)
Bibliographic Information
Gorenstein quotient singularities in dimension three
(Memoirs of the American Mathematical Society, no. 505)
American Mathematical Society, 1993
Available at 24 libraries
  Aomori
  Iwate
  Miyagi
  Akita
  Yamagata
  Fukushima
  Ibaraki
  Tochigi
  Gunma
  Saitama
  Chiba
  Tokyo
  Kanagawa
  Niigata
  Toyama
  Ishikawa
  Fukui
  Yamanashi
  Nagano
  Gifu
  Shizuoka
  Aichi
  Mie
  Shiga
  Kyoto
  Osaka
  Hyogo
  Nara
  Wakayama
  Tottori
  Shimane
  Okayama
  Hiroshima
  Yamaguchi
  Tokushima
  Kagawa
  Ehime
  Kochi
  Fukuoka
  Saga
  Nagasaki
  Kumamoto
  Oita
  Miyazaki
  Kagoshima
  Okinawa
  Korea
  China
  Thailand
  United Kingdom
  Germany
  Switzerland
  France
  Belgium
  Netherlands
  Sweden
  Norway
  United States of America
Note
"September 1993, volume 105, number 505 (end of volume)"--T.p
Includes bibliographical references (p. 86-88)
Description and Table of Contents
Description
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.
Table of Contents
Introduction Classification of finite subgroups of $SL(3,\mathbb C)$ The invariant polynomials and their relations of linear groups of $SL(3,\mathbb C)$ Gorenstein quotient singularities in dimension three.
by "Nielsen BookData"