On Rees algebras of linearly presented ideals

Let I   be a height two perfect ideal with a linear presentation matrix in a polynomial ring R=k[x1,…,xd]R=k[x1,…,xd]. Assume that μ(I)=d+1μ(I)=d+1 and I   satisfies the Artin–Nagata condition Gd−1Gd−1. We determine the defining ideal of the Rees algebra R(I)R(I) explicitly and we show that R(I)R(I) is Cohen–Macaulay.