相关论文: Castelnuovo-Mumford Regularity And Segre-Veronese …

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 A be a noetherian AS regular Koszul quiver algebra (if A is commutative, it is essentially a polynomial ring), and grA the category of finitely generated graded left A-modules. Following Jorgensen, we define the Castelnuovo-Mumford…

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,…

Matrix Schubert varieties are affine varieties arising in the Schubert calculus of the complete flag variety. We give a formula for the Castelnuovo-Mumford regularity of matrix Schubert varieties, answering a question of Jenna Rajchgot. We…

We investigate the asymptotic behaviour of Castelnuovo-Mumford regularity of Ext and Tor, with respect to the homological degree, over complete intersection rings. We derive from a theorem of Gulliksen a linearity result for the regularity…

Let $X \subseteq \mathbb{P}^r$ be a scroll of codimension $e$ and degree $d$ over a smooth projective curve of genus $g$. The purpose of this paper is to prove a linear Castelnuovo-Mumford regularity bound that reg$(X) \leq d-e+1+g(e-1)$.…

We introduce and study a notion of Castelnuovo-Mumford regularity suitable for scrolls obtained as projectivisations of sums of line bundles on $\mathbb P^m$. We show that this is a natural generalisation of the well known regularity on…

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 explore the relationship between multigraded Castelnuovo--Mumford regularity, truncations, Betti numbers, and virtual resolutions on a product of projective spaces $X$. After proving a uniqueness theorem for certain virtual resolutions,…

The Castelnuovo-Mumford regularity of a graded ring is an important invariant in computational commutative algebra, and there is increasing interest in multigraded generalizations. We study connections between two recent definitions of…

We compute the Castelnuovo-Mumford regularity of the edge ideals of two families of circulant graphs, which includes all cubic circulant graphs. A feature of our approach is to combine bounds on the regularity, the projective dimension, and…

Let $R=\oplus_{i\in \N_0}R_n$ be a standard graded ring, $R_+ :=\oplus_{i\in \N}R_n$ be the irrelevant ideal of $R$ and $\fa_0$ be an ideal of $R_0$. In this paper, as a generalization of the concept of Castelnouvo-Mumford regularity…

There are two motivation questions in \cite{MTS, MTS1} about Castelnuovo-Mumford regularity and vertex decomposable of simple graph $G$. In this paper, we disprove the questions by providing of two counterexamples.

The main goal of the paper is to generalize Castelnuovo-Mumford regularity for coherent sheaves on projective spaces to coherent sheaves on $n$-dimensional smooth projective varieties $X$ with an $n$-block collection $\cB $ which generates…

Let M be a complex of D-modules with bounded holonomic cohomology on a complex manifold. In this note, we prove that if the derived tensor product of M with itself is regular, then M is regular.

Let S = k[x_1,...,x_n] be a Z^r-graded ring with deg (x_i) = a_i \in Z^r for each i and suppose that M is a finitely generated Z^r-graded S-module. In this paper we describe how to find finite subsets of Z^r containing the multidegrees of…

The main result of this paper shows that the Castelnuovo-Mumford regularity of the tangent cone of a local ring is effectively bounded by the dimension and any extended degree. From this it follows that there are only a finite number of…

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.…

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.

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