First Coefficient ideals and R₁ property of Rees algebras

Let (A, m) be an excellent normal local ring of dimension d 2 with infinite residue field. Let I be an m-primary ideal. Then the following assertions are equivalent: (i) The extended Rees algebra AIt, t^-1 is R₁. (ii) The Rees algebra AIt is R₁. (iii) Proj (AIt) is R₁. (iv) (Iⁿ) ^* = (Iⁿ) ₁ for all n 1. Here (Iⁿ) ^* is the integral closure of Iⁿ and (Iⁿ) ₁ is the first coefficient ideal of Iⁿ.