Extremal Betti Numbers of Some Cohen-Macaulay Binomial Edge Ideals

We provide the regularity and the Cohen-Macaulay type of binomial edge ideals of Cohen-Macaulay cones,and we show the extremal Betti numbers of some classes of Cohen-Macaulay binomial edge ideals:Cohen-Macaulay bipartite and fan graphs.In addition,we compute the Hilbert-Poincaré series of the binomial edge ideals of some Cohen-Macaulay bipartite graphs.     

Castelnuovo–Mumford Regularity of Some Modules

We give bounds for the Castelnuovo–Mumford regularity of the so-called sequentially κ-Buchsbaum modules and of the canonical modules of certain rings.     

Castelnuovo–Mumford Regularity of Associated Graded Modules and Fiber Cones of Filtered Modules

We give bounds on the Castelnuovo–Mumford regularity of the associated graded module of an arbitrary good filtration and of its fiber cone. These bounds extend previous results of Rossi–Trung–Valla and Linh.     

On the Regularity of Codimension Two Surfaces and Threefolds with Singular Loci

ABSTRACT

For projective codimension two surfaces and threefolds whose singular locus is one dimensional, we get the sharp Castelnuovo–Mumford regularity bound in terms of degrees of defining equations and give the classification of nearly extremal cases. This is a generalization of the result of Bertram et al.     

Powers of ideals associated to (C4,2K2)-free graphs

Let G be a $(C_4,2K_2)$-free graph with edge ideal $I(G)?\mathbb{k}[x_1,\dots ,x_n]$. We show that $I{(G)}^s$ has linear resolution for every $s\ge 2$. Also, we show that every power of the vertex cover ideal of G has linear quotients. As a result, we describe the Castelnuovo–Mumford regularity of powers of $I{(G)}^{\vee }$ in terms of the maximum degree of G.     

Castelnuovo–Mumford Regularity and Gorensteinness of Fiber Cone

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.