## 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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