Related papers: Generators of Residual Intersections

Two families $\mathcal{F}$ and $\mathcal{G}$ of $k$-subsets of an $n$-set are called $s$-almost cross-$t$-intersecting if each member in $\mathcal{F}$ (resp. $\mathcal{G}$) is $t$-disjoint with at most $s$ members in $\mathcal{G}$ (resp.…

We show that any isometric action of a residually finite group admits approximate local finite models. As a consequence, if $G$ is residually finite, every isometric $G$-action embeds isometrically into a metric ultraproduct of finite…

We say that a set $A$ \emph{$t$-intersects} a set $B$ if $A$ and $B$ have at least $t$ common elements. Two families $\mathcal{A}$ and $\mathcal{B}$ are said to be \emph{cross-$t$-intersecting} if each set in $\mathcal{A}$ $t$-intersects…

A Magnus subgroup of a one-relator group is the free subgroup freely generated by a proper subset of the generators. Two such subgroups can intersect in the obvious way or in a larger, exceptional way. The condition of non-exceptional…

Two degenerate Poisson structures of the same rank possess a recursion operator if and only if their characteristic distributions coincide.

Let C be an irreducible projective curve of degree d in Pn(K), where K is an algebraically closed field, and let I be the associated homogeneous prime ideal. We wish to compute generators for I, assuming we are given sufficiently many…

In this paper we derive some conditions for transversal intersection of polynomial ideals. We exhibit some examples. Finally, as an application of the results proved, we compute the Betti numbers for ideals of the form $I_{1}(XY) + J$,…

We consider hyperplane arrangements generated by generic points and study their intersection lattices. These arrangements are known to be equivalent to discriminantal arrangements. We show a fundamental structure of the intersection…

It is shown that if $A$ is a regular local ring and $I$ is a maximally differential ideal in $A$, then $I$ is generated by an $A$-sequence.

A border basis scheme is an affine scheme that can be viewed as an open subscheme of the Hilbert scheme of \mu points of affine n-space. We study syzygies of the generators of a border basis scheme's defining ideal. These generators arise…

Let $M$ be a simple 3-manifold, and $F$ be a component of $\partial M$ of genus at least 2. Let $\alpha$ and $\beta$ be separating slopes on $F$. Let $M(\alpha)$ (resp. $M(\beta)$) be the manifold obtained by adding a 2-handle along…

We investigate the extent to which the exchange relation holds in finite groups $G$. We define a new equivalence relation $\equiv_{\mathrm{m}}$, where two elements are equivalent if each can be substituted for the other in any generating…

We prove that every quasi-complete intersection ideal is obtained from a pair of nested complete intersection ideals by way of a flat base change. As a by-product we establish a rigidity statement for the minimal two-step Tate complex…

Max cones are max-algebraic analogs of convex cones. In the present paper we develop a theory of generating sets and extremals of max cones in ${{\mathbb R}}_+^n$. This theory is based on the observation that extremals are minimal elements…

We consider homogeneous binomial ideals $I=(f_1,\ldots,f_n)$ in $K[x_1, \ldots, x_n]$, where $f_i = a_i x_i^{d_i} - b_i m_i$ and $a_i \neq 0$. When such an ideal is a complete intersection, we show that the monomials which are not divisible…

In the framework of Quark-Gluon String Model we calculate the inclusive spectra of secondaries produced in d+Au collisions at intermediate (CERN SPS) and at much higher (RHIC) energies. The results of numerical calculations at intermediate…

We study the existence and uniqueness of minimal supersolutions of backward stochastic differential equations with generators that are jointly lower semicontinuous, bounded below by an affine function of the control variable and satisfy a…

We compute the primary decomposition of certain ideals generated by subsets of minors in a generic matrix or in a generic symmetric matrix, or subsets of Pfaffians in a generic skew-symmetric matrix. Specifically, the ideals we consider are…

Over a field of characteristic $0$, we construct a minimal set of generators of the defining ideals of closures of nilpotent conjugacy class in the set of $n \times n$ matrices. This modifies a conjecture of Weyman and provides a complete…

We give several algorithms addressing computations of intersections of conjugate subgroups.