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Moduli of isolated hypersurface singularities. (English) Zbl 1084.32019
The author considers the problem of distinguishing between biholomorphically inequivalent hypersurface singularities on the basis of their corresponding moduli algebras. The moduli algebra of a complex hypersurface \(V\) in \(\mathbb C^n\) with an isolated singularity at the origin is defined as the quotient \(A=\mathbb C\{z_1,\dots, z_n\}/\langle f,\partial f/\partial z_1,\dots,\partial f/\partial z_n \rangle\). The author employs classical invariant theory to compute from \(A\) the \(j\)-invariant defined by K. Saito [Invent. Math. 23, 289–325 (1974; Zbl 0296.14019)]. As an application, the simple elliptic singularities \(\widetilde E_6\), \(\widetilde E_7\) and \(\widetilde E_8\) are analyzed.

32S25 Complex surface and hypersurface singularities
14J17 Singularities of surfaces or higher-dimensional varieties
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