X^p+Y^(p+1)+Z^(p+1)/Signaturen/Beispiel/en

Aus Wikiversity

We consider in characteristic the ring given by the equation

This is a normal hypersurface ring. This ring is not -pure, since , but . Hence it is not strongly -regular and so its -signature is . However, the differential signature is positive. This example is also an easy counterexample to the Zariski-Lipman conjecture.