When does the equality I2 QI hold true in Buchsbaum rings?

Let A be a Noetherian local ring with the maximal ideal and d dimA. Let Q be a parameter ideal in A and let I Q : . In this paper we shall study the problem of when the equality I2 QI holds true. K. Yamagishi [18, 19], the first author, and K. Nishida [9] have recently showed that the Rees algebras RI

n0 In, the associated graded rings GI RIIRI, and the fiber cones FI RIRI are all Buchsbaum rings with very specific graded local cohomology modules, if I2 QI and the base ring A is Buchsbaum. Our results will supply [18, 19] and [9] with ample examples.