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 A[It, t⁻¹] is R₁. (ii) The Rees algebra $A[It]$ is R₁. (iii) $Proj(A[It])$ 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.