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Auslander’s delta, the quasihomogeneity of isolated hypersurface singularities and the Tate resolution of the moduli algebra. (English) Zbl 0842.14027

Let \(R= S/ (f)\) be a complete isolated hypersurface singularity. We show that \(R\) is graded if and only if the Tate resolution of the moduli algebra \(R/ \overline {j(f)}\) is minimal. This criterion is based on the following general result: If the Tate resolution of a cyclic module of infinite projective dimension over a hypersurface ring is minimal then the \(\delta\)-invariant of (the completion of) that module is zero.

MSC:

14J17 Singularities of surfaces or higher-dimensional varieties
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