A V Jayanthan

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 (Formula Presented.), then the relation types of R(I) and FL(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.

In this article, we show that the depths of the associated graded ring and fiber cone of a lex-segment ideal in K[x,y] are equal. © 2010 Heldermann Verlag.

In this article, we study certain homological properties of the graded rings associated with stretched m-primary ideals in a Cohen-Macaulay local ring (A, m). We compute the h-polynomial of the fiber cone and using this expression we show that the fiber cone is Gorenstein is equivalent to being hypersurface under certain assumptions. We obtain some inequalities between the Hilbert coefficients of the fiber cone and obtain sufficient conditions for the equality.

Let G be a simple graph on n vertices and JG denote the binomial edge ideal of G in the polynomial ring S=K[x1,…,xn,y1,…,yn]. In this article, we compute the second graded Betti numbers of JG, and we obtain a minimal presentation of it when G is a tree or a unicyclic graph. We classify all graphs whose binomial edge ideals are almost complete intersection, prove that they are generated by a d-sequence and that the Rees algebra of their binomial edge ideal is Cohen-Macaulay. We also obtain an explicit description of the defining ideal of the Rees algebra of those binomial edge ideals.

In this article, we study the Castelnuovo-Mumford regularity and Gorenstein properties of the fiber cone. We obtain upper bounds for the Castelnuovo-Mumford regularity of the fiber cone and obtain sufficient conditions for the regularity of the fiber cone to be equal to that of the Rees algebra. We obtain a formula for the canonical module of the fiber cone and use it to study the Gorenstein property of the fiber cone. © 2012 Copyright Taylor and Francis Group, LLC.