Related papers: Multigraded modules of Borel type

Generalizing techniques that prove that Veronese subrings are Koszul, we show that Rees and multi-Rees algebras of certain types of principal strongly stable ideals are Koszul. We provide explicit Gr\"obner basis for the defining ideals of…

In ``Cohen--Macaulay rings'' Bruns and Herzog define the graded canonical module for $\mathbb{Z}^r$-graded rings. We generalize the definition to multigradings and prove that the canonical module ``localizes''. As an application, we give a…

We compute the minimal primary decomposition for completely squarefree lexsegment ideals. We show that critical squarefree monomial ideals are sequentially Cohen-Macaulay. As an application, we give a complete characterization of the…

We introduce cell modules for the tabular algebras defined in a previous work (math.QA/0107230); these modules are analogous to the representations arising from left Kazhdan--Lusztig cells. The standard modules of the title are constructed…

Based upon properties of ordinal length, we introduce a new class of modules, the binary modules, and study their endomorphism ring. The nilpotent endomorphisms form a two-sided ideal, and after factoring this out, we get a commutative…

In this paper, we study a special type of ultrafilter which we call Shelah ultrafilter. We show that it is possible to add a Shelah ultrafilter using a special forcing notion. We also show that Shelah ultrafilters turn out to be…

We prove that the multi-Rees algebra $\mathcal{R}(I_1 \oplus \cdots \oplus I_r)$ of a collection of strongly stable ideals $I_1, \ldots, I_r$ is of fiber type. In particular, we provide a Gr\"obner basis for its defining ideal as a union of…

We establish a relationship between the graded quotients of a filtered holonomic D-module, their sheaf-theoretic duals, and the characteristic variety, in case the filtered D-module underlies a polarized Hodge module on a smooth algebraic…

Let $k$ be a field. We determine the ideals $I$ in a finitely generated graded $k$-algebra $A$, whose associated graded rings are isomorphic to $A$. Also we compute the graded local cohomologies of the Rees rings $A[I t]$ and give the…

Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring over the field $K$, and let $I\subset S$ be a graded ideal. It is shown that the higher iterated Hilbert coefficients of the graded $S$-modules $\Tor_i^S(M,I^k)$ and $\Ext^i_S(M,I^k)$ are…

In Finite Group Modular Representation Theory, the basic objects are the indecomposable and simple modules. This paper offers a new classification of these objects that refines the Green Theory Classification of indecomposable and simple…

In this paper, we complete the classification of the {\bf Z}-graded modules of the intermediate series over the $q$-analog Virasoro-like algebra $L$. We first construct four classes of irreducible {\bf Z}-graded $L$-modules of the…

In this article we construct a new class of finite dimensional irreducible modules genaralizing evaluation modules for multiloop superalgebra of type A(m,n) and C(m). We prove that these are the only such modules. In all other cases it is…

Let $R$ be a Cohen-Macaulay local domain. In this paper we study the cone of Cohen-Macaulay modules inside the Grothendieck group of finitely generated $R$-modules modulo numerical equivalences, introduced in \cite{CK}. We prove a result…

A quandle equipped with a good involution is referred to as symmetric. It is known that the cohomology of symmetric quandles gives rise to strong cocycle invariants for classical and surface links, even when they are not necessarily…

For a wide class of Cohen--Macaulay modules over the local ring of the plane curve singularity of type T_44 we explicitly describe the corresponding matrix factorizations. The calculations are based on the technique of matrix problems, in…

In this paper, we introduce the notion of completely non-trivial module of a Lie conformal algebra. By this notion, we classify all finite irreducible modules of a class of $\mathbb{Z}^+$-graded Lie conformal algebras…

We introduce a new class of graded rings extending the class of generalized Weyl algebras. These rings are orders in crossed products of the most general type, and we introduce their basic structure theory. We provide an extensive list of…

Triangular modular curves are a generalization of modular curves that arise from quotients of the upper half-plane by congruence subgroups of hyperbolic triangle groups. These curves also arise naturally as a source of Belyi maps with…

We solve a long standing open problem concerning the structure of finite cycles in the category mod A of finitely generated modules over an arbitrary artin algebra A, that is, the chains of homomorphisms $M_0 \stackrel{f_1}{\rightarrow} M_1…