Classes of projectively equivalent quadrics over local rings

摘要

We study quadrics and quadratic forms in a projective space over a local ring R = 2R whose maximal ideal is principal and nilpotent. The problem of enumeration of classes of projectively equivalent quadrics is completed for |R~* : R~(*2)| = 2; when |R~* : R~(*2)| = 4, the problem is solved together with the enumeration problem of classes of projectively congruent quadrics under an additional condition.