Gorenstein quotient singularities in dimension three
著者
書誌事項
Gorenstein quotient singularities in dimension three
（Memoirs of the American Mathematical Society, no. 505）
American Mathematical Society, 1993
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注記
"September 1993, volume 105, number 505 (end of volume)"--T.p
Includes bibliographical references (p. 86-88)
内容説明・目次
内容説明
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.
目次
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.
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