Related papers: Divisors on Rational Normal Scrolls

Let G be a real, connected, noncompact, semisimple Lie group, let K be a maximal compact subgroup of G, and let g=k+p be the corresponding Cartan decomposition of the complexified Lie algebra of G. Sequences of strongly orthogonal…

We give an algorithm to determine finitely many generators for a subgroup of finite index in the unit group of an integral group ring $\mathbb{Z} G$ of a finite nilpotent group $G$, this provided the rational group algebra $\mathbb{Q} G$…

We show that for any two proper monomial ideals I and J in the polynomial ring S = k[x_1, ..., x_n] the ring S/IJ is Golod. We also show that if I is squarefree then for large enough k the quotient S/I^{(k)} of S by the kth symbolic power…

Let $G$ be a simple graph on $d$ vertices. We define a monomial ideal $K$ in the Stanley-Reisner ring $A$ of the order complex of the Boolean algebra on $d$ atoms. The monomials in $K$ are in one-to-one correspondence with the proper…

This work is about symbolic powers of codimension two perfect ideals in a standard polynomial ring over a field, where the entries of the corresponding presentation matrix are general linear forms. The main contribution of the present…

Let $K$ be a field and $G$ be a finite group. Let $G$ act on the rational function field $K(x(g):g\in G)$ by $K$-automorphisms defined by $g\cdot x(h)=x(gh)$ for any $g,h\in G$. Denote by $K(G)$ the fixed field $K(x(g):g\in G)^G$. Noether's…

This paper is an MGM version of arXiv.org:1703.04266 and arXiv:1907.03364, and a follow-up to Section 5 of arXiv:1503.05523. In the setting of a commutative ring $S$ with a weakly proregular finitely generated ideal $J\subset S$, we…

We study the rings of invariants for the indecomposable modular representations of the Klein four group. For each such representation we compute the Noether number and give minimal generating sets for the Hilbert ideal and the field of…

We establish formulas for computation of the higher algebraic $K$-groups of the endomorphism rings of objects linked by a morphism in an additive category. Let ${\mathcal C}$ be an additive category, and let $Y\ra X$ be a covariant morphism…

Let $R$ be a normal Noetherian local domain of Krull dimension two. We examine intersections of rank one discrete valuation rings that birationally dominate $R$. We restrict to the class of prime divisors that dominate $R$ and show that if…

Let $R:= \Bbbk[x_1,\ldots,x_{n}]$ be a polynomial ring over a field $\Bbbk$, $I \subset R$ be a homogeneous ideal with respect to a weight vector $\omega = (\omega_1,\ldots,\omega_n) \in (\mathbb{Z}^+)^n$, and denote by $d$ the Krull…

Let $k$ be an algebraically closed field of characteristic $0$. Let $X$ be a $2\times e$ matrix of linear forms over a polynomial ring $k[\mathsf{x}_1, \ldots,\mathsf{x}_n]$ (where $e,n\ge 1$). We prove that the determinantal ring $R =…

In this paper we prove that a classical theorem by McAdam about the analytic spread of an ideal in a Noetherian local ring continues to be true for divisorial filtrations on a two dimensional normal excellent local ring $R$, and that the…

The quantum Euclidean spheres, $S_q^{N-1}$, are (noncommutative) homogeneous spaces of quantum orthogonal groups, $\SO_q(N)$. The *-algebra $A(S^{N-1}_q)$ of polynomial functions on each of these is given by generators and relations which…

We investigate the minimal number of generators $\mu$ and the depth of divisorial ideals over normal semigroup rings. Such ideals are defined by the inhomogeneous systems of linear inequalities associated with the support hyperplanes of the…

Let $S = K[x_1,..., x_n]$ be a polynomial ring over a field $K$. Let $I(G) \subseteq S$ denote the edge ideal of a graph $G$. We show that the $\ell$th symbolic power $I(G)^{(\ell)}$ is a Cohen-Macaulay ideal (i.e., $S/I(G)^{(\ell)}$ is…

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…

Let $(V,q)$ be a non-degenerate $n$-dimensional quadratic space over the rationals of real signature $(r,s)$. For every integer $1\leq k \leq \min\{r,n-2\}$ we construct classes in the cohomology of arithmetic subgroups of $\mathrm{O}(V)$…

Let $K$ be an algebraically closed field of characteristic $0$ and let $G$ be a finite cyclic group of order $n$. In this note we prove, using induction on the number of prime divisors of $n$, that $R_K(G)/I \cong \mathbb{Z}[X]/\langle…

Given a normal toric algebra $R$, we compute a uniform integer $D = D(R) > 0$ such that the symbolic power $P^{(D N)} \subseteq P^N$ for all $N >0$ and all monomial primes $P$. We compute the multiplier $D$ explicitly in terms of the…