On the Relation Type of Fiber Cone

Abstract

In this article, we study the relation type of the fiber cone of certain special classes of ideals in Noetherian local rings. We show that in any Noetherian local ring, if deviation of I is 1, and depth $(G(\mathcal F_{L})) \geq \ell -1$ , then the relation types of $\mathcal {R}(I)$ and F L (I) are equal. We also prove that for lexsegment ideals in K[x,y], where K is a field, the relation types of the fiber cone and the Rees algebra are equal.