Connectivity through bounds for the Castelnuovo-Mumford regularity

Bounds for the Regularity of Edge Ideal of Vertex Decomposable and Shellable Graphs

Castelnuovo-Mumford regularity of products of monomial ideals

Let $R=k[x_1,x_2,cdots, x_N]$ be a polynomial ring over a field $k$. We prove that for any positive integers $m, n$, $text{reg}(I^mJ^nK)leq mtext{reg}(I)+ntext{reg}(J)+text{reg}(K)$ if $I, J, Ksubseteq R$ are three monomial complete intersections ($I$, $J$, $K$ are not necessarily proper ideals of the polynomial ring $R$), and $I, J$ are of the form $(x_{i_1}^{a_1}, x_{i_2}^{a_2}, cdots, x_{i_l...

Castelnuovo-Mumford regularity of canonical and deficiency modules

We give two kinds of bounds for the Castelnuovo-Mumford regularity of the canonical module and the deficiency modules of a ring, respectively in terms of the homological degree and the Castelnuovo-Mumford regularity of the original ring.

Asymptotic Linear Bounds for the Castelnuovo-mumford Regularity

We prove asymptotic linear bounds for the Castelnuovo-Mumford regularity of certain filtrations of homogeneous ideals whose Rees algebras need not be Noetherian.

Castelnuovo-mumford Regularity of Ext Modules and Homological Degree

Bounds for the Castelnuovo-Mumford regularity of Ext modules, over a polynomial ring over a field, are given in terms of the initial degrees, Castelnuovo-Mumford regularities and number of generators of the two graded modules involved. These general bounds are refined in the case the second module is the ring. Other estimates, for instance on the size of graded pieces of these modules, are give...