Asymptotic Linear 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.

Castelnuovo-mumford Regularity by Approximation

The Castelnuovo-Mumford regularity of a module gives a rough measure of its complexity. We bound the regularity of a module given an approximation by modules whose regularities are known. Such approximations can arise naturally for modules constructed by inductive combinatorial means. We apply these methods to bound the regularity of ideals constructed as combinations of linear ideals and the m...

. A C ] 9 S ep 2 00 3 CASTELNUOVO - MUMFORD REGULARITY BY APPROXIMATION

The Castelnuovo-Mumford regularity of a module gives a rough measure of its complexity. We bound the regularity of a module given a system of approximating modules whose regularities are known. Such approximations can arise naturally for modules constructed by inductive combinatorial means. We apply these methods to bound the regularity of ideals constructed as combinations of linear ideals and...