Multiplicity of the special fiber of blowups

Let (R,m) be a local Cohen-Macaulay ring and let I be an m-primary ideal. In this paper we give sharp bounds on the multiplicity of the special fiber ring ℱ of I in terms of other well-known invariants of I. Special attention is then paid in studying when equality holds in these bounds, with a particular interest in the unmixedness or, better, the Cohen-Macaulayness of ℱ.