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VOL. 43 | 2010 Simple Elliptic Hypersurface Singularities: A New Look at the Equivalence Problem
Alexander Isaev

Editor(s) Toshizumi Fukui, Adam Harris, Alexander Isaev, Satoshi Koike, Laurentiu Paunescu


Let $V_1, V_2$ be hypersurface germs in $\mathbb C^m$, with $m \geq 2$, each having a quasi-homogenous isolated singularity at the origin. In our recent joint article with G. Fels, W. Kaup and N. Kruzhilin we reduced the biholomorphic equivalence problem for $V_1, V_2$ to verifying whether certain polynomials arising from the moduli algebras of $V_1, V_2$ are equivalent up to scale by means of a linear transformation. In the present we illustrate this result by the examples of simple elliptic singularities of $types \tilde{E}_6, \tilde{E}_7, \tilde{E}_8$ and compare our method with that due to M. G. Eastwood who has also introduced certain polynomials that distinguish non-equivalent singularities within each of these three types.


Published: 1 January 2010
First available in Project Euclid: 18 November 2014

zbMATH: 1228.32029
MathSciNet: MR2763232

Rights: Copyright © 2010, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University. This book is copyright. Apart from any fair dealing for the purpose of private study, research, criticism or review as permitted under the Copyright Act, no part may be reproduced by any process without permission. Inquiries should be made to the publisher.


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