Related papers: Castelnuovo-Mumford regularity bounds for singular…

Castelnuovo-Mumford regularity is an important invariant of projective algebraic varieties. A well known conjecture due to Eisenbud and Goto gives a bound for regularity in terms of the codimension and degree. This conjecture is known to be…

We show that the Eisenbud-Goto conjecture holds for (homogeneous) seminormal simplicial affine semigroup rings. Moreover, we prove an upper bound for the Castelnuovo-Mumford regularity in terms of the dimension, which is similar as in the…

The purpose of this paper is to establish a Castelnuovo-Mumford regularity bound for threefolds with mild singularities. Let $X$ be a non-degenerate normal projective threefold in $\mathbb{P}^r$ of degree $d$ and codimension $e$. We prove…

Castelnuovo-Mumford regularity is an important invariant of projective algebraic varieties. A well known conjecture due to Eisenbud and Goto gives a bound for regularity in terms of the codimension and degree,i.e., Castelnuovo-Mumford…

We bound the Castelnuovo-Mumford regularity and syzygies of the ideal of the singular set of a plane curve, and more generally of the conductor scheme of certain projectively Gorenstein varieties.

We establish upper bounds for the Castelnuovo--Mumford regularity of the coordinate ring of a simplicial projective toric variety with at most one singular point. In the smooth case, our results recover the bound of Herzog and Hibi [Proc.…

McCullough and Peeva found sequences of counterexamples to the Eisenbud--Goto conjecture on the Castelnuovo--Mumford regularity by using Rees-like algebras, where entries of each sequence have increasing dimensions and codimensions. In this…

Castelnuovo-Mumford regularity is a measure of algebraic complexity of an ideal. Regularity of monomial ideals can be investigated combinatorially. We use a simple graph decomposition and results from structural graph theory to prove,…

Castelnuovo-Mumford regularity is an important invariant of projective algebraic varieties. A well known conjecture due to Eisenbud and Goto gives a bound for regularity in terms of the codimension and degree,i.e., Castelnuovo-Mumford…

Let $X \subseteq \mathbb{P}^r$ be a non-degenerate smooth projective variety of dimension $n$, codimension $e$, and degree $d$ defined over an algebraically closed field of characteristic zero. In this paper, we first show that $\text{reg}…

Let $X\subseteq \mathbb{P}^N$ be a non-degenerate normal projective variety of codimension $e$ and degree $d$ with isolated $\mathbb{Q}$-Gorenstein singularities. We prove that the Castelnuovo-Mumford regularity…

In this paper we prove the Eisenbud-Goto conjecture for connected curves. We also investigate the structure of connected curves for which this bound is optimal. In particular, we construct connected curves of arbitrarily high degree in…

We show that bounds on the Castelnuovo-Mumford regularity of singular schemes, as a function of the degrees of the equations defining the shceme, of its dimension and of the dimension of their singular space. In the case where the…

A long standing conjecture, known to us as the Eisenbud Goto conjecture, states that an n-dimensional variety embedded with degree $d$ in the $N$- dimensional projective space is $(d-(N-n)+1)$-regular in the sense of Castelnuovo-Mumford. In…

We introduce and study a notion of Castelnuovo-Mumford regularity suitable for rational normal scroll surfaces. In this setting we prove analogs of some classical properties. We prove splitting criteria for coherent sheaves and a…

We compare, for smooth monomial projective curves, the Castel- nuovo-Mumford regularity and the reduction number; we present an example where these two numbers differ. However, we show they coin- cide for a certain class of monomial curves.…

When M is a finitely generated graded module over a standard graded algebra S and I is an ideal of S, it is known from work of Cutkosky, Herzog, Kodiyalam, R\"omer, Trung and Wang that the Castelnuovo-Mumford regularity of I^mM has the form…

In this article we establish bounds for the Castelnuovo-Mumford regularity of projective schemes in terms of the degrees of their defining equations. The main new ingredient in our proof is to show that generic residual intersections of…

It is well known that the Eisenbud-Goto regularity conjecture is true for arithmetically Cohen-Macaulay varieties, projective curves, smooth surfaces, smooth threefolds in $\mathbb{P}^5$, and toric varieties of codimension two. After J.…

In this note, we give a bound for the Castelnuovo-Mumford regularity of a homogeneous ideal $I$ in terms of the degrees of its generators. We assume that $I$ defines a local complete intersection with log canonical singularities.