On the relation type of fiber cone (Q746811)

Let \(I\) be an ideal in a Noetherian ring. The authors consider the Fiber Cone \(F(I)\) and the Rees algebra \({\mathcal R}(I)\) associated to \(I\), and study the relation type of these two algebras. First they prove that if \(I\) is a lexsegment ideal in a ring in two variables, then \(\operatorname{reltype}(F(I)) = \operatorname{reltype}({\mathcal R}(I))\). Moreover they study equimultiple ideals of deviation \(1\), that is, ideals \(I\) such that height\((I)\) is equal to the analytic spread \(\ell\) of \(I\), and \(I\) is generated by \(\ell+1\) elements. They give a sufficient condition on the ideals in this class, to have \(\operatorname{reltype}(F(I)) = \operatorname{reltype}({\mathcal R}(I))\).