Related papers: The regularity of points in multi-projective space…

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…

In this paper we show that the sets of $F$-jumping coefficients of ideals form discrete sets in certain graded $F$-finite rings. We do so by giving a criterion based on linear bounds for the growth of the Castelnuovo-Mumford regularity of…

Let $G$ be a simple graph and $I(G)$ be its edge ideal. In this article, we study the Castelnuovo-Mumford regularity of symbolic powers of edge ideals of join of graphs. As a consequence, we prove Minh's conjecture for wheel graphs,…

In this paper, we study the Castelnuovo-Mumford regularity of nonlinearly normal embedding of rational surfaces. Let $X$ be a rational surface and let $L \in {Pic}X$ be a very ample line bundle. For a very ample subsystem $V \subset H^0…

For a polynomial ring S in n variables, we consider the natural action of the symmetric group S_n on S by permuting the variables. For an S_n-invariant monomial ideal I in S and j >= 0, we give an explicit recipe for computing the modules…

For a partition $\lambda$ of $n \in {\mathbb N}$, let $I^{\rm Sp}_\lambda$ be the ideal of $R=K[x_1,\ldots,x_n]$ generated by all Specht polynomials of shape $\lambda$. In the previous paper, the second author showed that if $R/I^{\rm…

The Castelnuovo-Mumford regularity of varieties of degree r and dimension n in the r-dimensional projective space that have an extremal secant line, is at least d-r+n+1. We classify these varieties and show that their regularity is exactly…

Consider a measure $\mu_\lambda = \sum_x \xi_x \delta_x$ where the sum is over points $x$ of a Poisson point process of intensity $\lambda$ on a bounded region in $d$-space, and $\xi_x$ is a functional determined by the Poisson points near…

Toward a partial classification of monomial ideals with $d$-linear resolution, in this paper, some classes of $d$-uniform clutters which do not have linear resolution, but every proper subclutter of them has a $d$-linear resolution, are…

Ideals generated by pfaffians are of interest in commutative algebra and algebraic geometry, as well as in combinatorics. In this article we compute multiplicity and Castelnuovo-Mumford regularity of pfaffian ideals of ladders. We give…

We prove the optimal $C^{1,1}$ regularity of the volume function on the big cone of a projective manifold, and investigate its regularity when restricted to segments moving in ample directions.

Let $I$ be a homogeneous ideal in a polynomial ring $S$. In this paper, we extend the study of the asymptotic behavior of the minimum distance function $\delta_I$ of $I$ and give bounds for its stabilization point, $r_I$, when $I$ is an…

In this paper we prove that for any definable subset $X\subset \mathbb{R}^{n}$ in a polynomially bounded o-minimal structure, with $dim(X)<n$, there is a finite set of regular projections (in the sense of Mostowski ). We give also a weak…

Let $R$ be a standard graded algebra over a field $k$. We prove an Auslander-Buchsbaum formula for the absolute Castelnuovo-Mumford regularity, extending important cases of previous works of Chardin and R\"omer. For a bounded complex of…

In a previous paper we developed a regularity and compactness theory in Euclidean ambient spaces for codimension 1 weakly stable CMC integral varifolds satisfying two (necessary) structural conditions. Here we generalize this theory to the…

In this paper we consider the problem of determining the Hilbert function of schemes X of the proiective space P^n which are the generic union of s lines and one m-multiple point. We completely solve this problem for any s and m when n > 3.…

We study bounds for the Castelnuovo-Mumford regularity of homogeneous ideals in a polynomial ring in terms of the number of variables and the degree of the generators. In particular our aim is to give a positive answer to a question posed…

We study chains of nonzero edge ideals that are invariant under the action of the monoid $\mathrm{Inc}$ of increasing functions on the positive integers. We prove that the sequence of Castelnuovo--Mumford regularity of ideals in such a…

We will give an upper bound for the $k$-normality of very ample lattice simplices, and then give an Eisenbud-Goto-type bound for some special classes of projective toric varieties.

Given positive integers $m_1, m_2, ..., m_n$, and $n$ general points $p_i$ of ${\bf CP}^2$, bounds are given for the least degree $t$ among plane curves passing through each point $p_i$ with multiplicity at least $m_i$, and for the least…