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Gorenstein Isolated Quotient Singularities Over ℂ

Published online by Cambridge University Press:  16 April 2014

D. A. Stepanov
D. A. Stepanov*
Affiliation:
Department of Mathematical Modelling, Bauman Moscow State Technical University, 2-ya Baumanskaya ul. 5, Moscow 105005, Russia, (xlink:href="[email protected]">[email protected])
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Abstract

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In this paper we review the classification of isolated quotient singularities over the field of complex numbers due to Zassenhaus, Vincent and Wolf. As an application, we describe Gorenstein isolated quotient singularities over ℂ, generalizing a result of Kurano and Nishi.

Keywords

Gorenstein singularityquotient singularitygroups without fixed pointsPrimary 14B05
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 3 , October 2014 , pp. 811 - 839
Copyright
Copyright © Edinburgh Mathematical Society 2014 

References

1.Akhiezer, D. N., Lie group actions in complex analysis, Aspects of Mathematics, Volume 27 (Vieweg, Braunschweig, 1995).CrossRefGoogle Scholar
2.Atiyah, M. F. and Macdonald, I. G., Introduction to commutative algebra (Addison-Wesley, 1969).Google Scholar
3.Benson, D. J., Polynomial invariants of finite groups, London Mathematical Society Lecture Note Series, Volume 190 (Cambridge University Press, 1993).Google Scholar
4.Curtis, C. and Reiner, J., Representation theory of finite groups and associative algebras, American Mathematical Society Chelsea Publishing Series, Volume 356 (American Mathematical Society, Providence, RI, 1962).Google Scholar
5.Eisenbud, D., Commutative algebra with a view toward algebraic geometry, Graduate Texts in Mathematics, Volume 150 (Springer, 1995).Google Scholar
6.Klein, F., Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen von fünften Grade (Leipzig, 1884).Google Scholar
7.Kurano, K. and Nishi, S., Gorenstein isolated quotient singularities of odd prime dimension are cyclic, Commun. Alg. 40(8) (2012), 3010–3020.CrossRefGoogle Scholar
8.Popov, V. L., When are the stabilizers of all nonzero semisimple points finite?, in Operator algebras, unitary representations, enveloping algebras and invariant theory, Progress in Mathematics, Volume 92, pp. 541–559 (Birkhäuser, 1990).Google Scholar
9.Serre, J.-P., Representations linéaires des groupes finis (Hermann, Paris, 1967).Google Scholar
10.Suzuki, M., On finite groups with cyclic Sylow subgroups for all odd primes, Am. J. Math. 77 (1955), 657–691.CrossRefGoogle Scholar
11.Vincent, G., Les groupes lineares finis sans points fixes, Comment. Math. Helv. 20 (1947), 117–171.Google Scholar
12.Watanabe, K.-I., Certain invariant subrings are Gorenstein, I, Osaka J. Math. 11(1) (1974), 1–8.Google Scholar
13.Watanabe, K.-I., Certain invariant subrings are Gorenstein, II, Osaka J. Math. 11(2) (1974), 379–388.Google Scholar
14.Wolf, J. A., Spaces of constant curvature, 6th edn (American Mathematical Society, Providence, RI, 2011).Google Scholar
15.Zassenhaus, H., Über endliche Fastkörper, Abh. Math. Sem. Univ. Hamburg 11 (1935), 187–220.Google Scholar