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Item Details
| Title:
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GORENSTEIN QUOTIENT SINGULARITIES IN DIMENSION THREE
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| By: |
Stephen Shing-Taung Yau, Yu Yung |
| Format: |
Paperback |
| List price:
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£33.95 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
0821825674 |
| ISBN 13: |
9780821825679 |
| Publisher: |
AMERICAN MATHEMATICAL SOCIETY |
| Pub. date: |
15 September, 1993 |
| Series: |
Memoirs of the American Mathematical Society No. 505 |
| Pages: |
88 |
| 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 $S\!L(3,{\mathbb C})$. This book presents the classification of finite subgroups of $S\!L(3,{\mathbb C})$, including two types, (J) and (K). |
| Synopsis: |
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. |
| Publication: |
US |
| Imprint: |
American Mathematical Society |
| Returns: |
Returnable |
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