E 8-Gleichung/x nicht in (y,z)^*/Erzwingende Algebra/Beispiel/en

Let be a field of positive characteristic and consider the ring

together with the ideal and . Since has a rational singularity, it is -regular, i.e. all ideals are tightly closed. Therefore and so the torsor

is an affine scheme. In characteristic zero this can be proved by either using that is a quotient singularity or by using the natural grading () where the corresponding cohomology class gets degree and then applying the geometric criteria on the corresponding projective curve (rather the corresponding curve of the standard-homogenization ).