Abstract | Let R=circled plusi≥0Ri be an Artinian standard graded K-algebra defined by quadrics. Assume that dimR2≤3 and that K is algebraically closed, of characteristic ≠2. We show that R is defined by a Gröbner basis of quadrics with, essentially, one exception. The exception is given by K[x,y,z]/I where I is a complete intersection of three quadrics not containing a square of a linear form. |