Related papers: A remark on symbolic powers

We study $p$-harmonic maps, $p$-harmonic morphisms, biharmonic maps, and quasiregular mappings into submanifolds of warped product Riemannian manifolds ${I}\times_f S^{m-1}(k)\, $ of an open interval and a complete simply-connecteded…

Let $I$ be the ideal generated by the maximal minors of a matrix of indeterminates over a field and let $J$ denote the generic link, i.e., the most general link, of $I$. The generators of the ideal $J$ are not known. We provide an explicit…

This paper studies properties of simplicial complexes for which the m-th symbolic power of the Stanley-Reisner ideal equals to the m-th ordinary power for a given m > 1. The main results are combinatorial characterizations of such complexes…

In this paper we study a representation problem first considered in a simpler version by Bank and El Karoui [2004]. A key ingredient to this problem is a random measure $\mu$ on the time axis which in the present paper is allowed to have…

In this note we consider compactifications of ${\cal M}$-theory on $Spin(7)$-holonomy manifolds to three-dimensional Minkowski space. In these compactifications a warp factor is included. The conditions for unbroken N=1 supersymmetry give…

For an ideal $I\subseteq\mathbb{R}[x]$ given by a set of generators, a new semidefinite characterization of its real radical $I(V_\mathbb{R}(I))$ is presented, provided it is zero-dimensional (even if $I$ is not). Moreover we propose an…

We study the symbolic powers of the Stanley-Reisner ideal $I_{B_n}$ of a bipyramid $B_n$ over a $n-$gon $Q_n$. Using a combinatorial approach, based on analysis of subtrees in $Q_n$ we compute the Waldschmidt constant of $I_{B_n}$.

In this paper, the containment problem for the defining ideal of a special type of zero dimensional subschemes of $\mathbb{P}^2$, so called quasi star configurations, is investigated. Some sharp bounds for the resurgence of these types of…

Let $S=\mathbb{K}[x_1,\ldots, x_n]$ be the polynomial ring over a field $\mathbb{K}$ and $\mathfrak{m}= (x_1, \ldots, x_n)$ be the irredundant maximal ideal of $S$. For an ideal $I \subset S$, let $\mathrm{sat}(I)$ be the minimum number $k$…

Can there be a structure space-type theory for an arbitrary class of ideals of a ring? The ideal spaces introduced in this paper allows such a study and our theory includes (but not restricted to) prime, maximal, minimal prime, strongly…

Let $S$ be a regular local ring or a polynomial ring over a field and $I$ be an ideal of $S$. Motivated by a recent result of Herzog and Huneke, we study the natural question of whether $I^m$ is a Golod ideal for all $m\geq 2$. We observe…

This paper establishes the fundamental properties of the $s$-closures, a recently introduced family of closure operations on ideals of rings of positive characteristic. The behavior of the $s$-closure of homogeneous ideals in graded rings…

The Geometrical Lemma is a classical result in the theory of (complex) smooth representations of $p$-adic reductive groups, which helps to analyze the parabolic restriction of a parabolically induced representation by providing a filtration…

Let $R = \mathbb{K}[x_1, \ldots, x_n]$ be a polynomial ring over a field $\mathbb{K}$, and let $I \subseteq R$ be a monomial ideal of height $h$. We provide a formula for the multiplicity of the powers of $I$ when all the primary ideals of…

One of the most fundamental mathematical contributions of Garrett Birkhoff is the HSP theorem, which implies that a finite algebra B satisfies all equations that hold in a finite algebra A of the same signature if and only if B is a…

Let I be a finitely supported complete m-primary ideal of a regular local ring (R, m). A theorem of Lipman implies that I has a unique factorization as a *-product of special *-simple complete ideals with possibly negative exponents for…

\emph{Minkowski rings} are certain rings of simple functions on the Euclidean space $W = {\mathbb{R}}^d$ with multiplicative structure derived from Minkowski addition of convex polytopes. When the ring is (finitely) generated by a set…

We show that if a semipositive symplectic manifold $M^{2n}$ is Steenrod uniruled, in the sense that the quantum Steenrod power of the point class does not agree with its classical Steenrod power for any prime, then the (rational) quantum…

Let $\Sigma$ be a finite collection of linear forms in $\mathbb K[x_0,\ldots,x_n]$, where $\mathbb K$ is a field. Denote ${\rm Supp}(\Sigma)$ to be the set of all nonproportional elements of $\Sigma$, and suppose ${\rm Supp}(\Sigma)$ is…

We use pseudodeformation theory to study the analogue of Mazur's Eisenstein ideal with certain squarefree levels. Given a prime number $p>3$ and a squarefree number $N$ satisfying certain conditions, we study the Eisenstein part of the…