Buch, Englisch, 88 Seiten, Format (B × H): 180 mm x 255 mm, Gewicht: 192 g
Buch, Englisch, 88 Seiten, Format (B × H): 180 mm x 255 mm, Gewicht: 192 g
ISBN: 978-0-8218-2567-9
Verlag: American Mathematical Society
If $G$ is a finite subgroup of $GL(3,{\Bbb C )$, then $G$ acts on ${\Bbb C 3$, and it is known that ${\Bbb C 3/G$ 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 ${\Bbb C 3/G$ 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.
Written for readers with a background in abstract algebra and elementary complex variety theory, this self-contained book provides an explicit classification of all finite subgroups in SL(3,C). Yau and Yu present a general method for finding invariant polynomials and their relations to finite subgroups of GL(3,C) and also find minimal quotient generators of the ring of invariant polynomials and relations among them. This book is directed towards advanced undergraduate students, graduate students, and researchers.
