A class of perfect determinantal ideals

In recent years several authors [ l ] , [2], [4], [13], [17], [18] have studied the special homological properties of ideals generated by the subdeterminants of a matrix or "determinantal" ideals. The question of whether the ideal of m + 1 by m + 1 minors of an r by 5 matrix is perfect if the grade is as large as possible, (r—m)(s — m), has remained open, although the special cases m = 0, 1, and r—1 (r^s) are known. The general result is Corollary 4 of Theorem 1. For purposes of the induction argument used to prove the theorem it is necessary to consider a larger class of ideals somewhat complicated to describe.