This paper presents the rudiments of Hilbert-Mumford Intersection (HMI) theory: intersection theory on the relative Hilbert scheme of a family of nodal (or smooth) curves, over a base of arbitrary dimension. We introduce an additive group of geometric cycles, called ’tautological module’, generated by diagonal loci, node scrolls, and twists thereof. We determine recursively the intersection act...

we investigate the problem of the existence of a frame forright ideals of a c*-algebra a, without the use of the kasparov stabilizationtheorem. we show that this property can not characterize a as a c*-algebraof compact operators.

The purpose of this paper is to initiate a new attack on Arveson’s resistant conjecture, that all graded submodules of the d-shift Hilbert module H are essentially normal. We introduce the stable division property for modules (and ideals): a normed module M over the ring of polynomials in d variables has the stable division property if it has a generating set {f1, . . . , fk} such that every h ...

Let τ be a linear map from a unital C∗-algebra A to a von Neumann algebra B and let C be a unital C∗-algebra. A map T from a Hilbert A-module E to a von Neumann C-B module F is called a τ -map if 〈T (x), T (y)〉 = τ(〈x, y〉) for all x, y ∈ E. A Stinespring type theorem for τ -maps and its covariant version are obtained when τ is completely positive. We show that there is a bijective correspondenc...

The denominator of the Hilbert series of a finitely generated R-module M does not always divide the denominator of the Hilbert series of R. For this reason, we define the universal denominator. The universal denominator of a module M is the least common multiple of the denominators of the Hilbert series of all submodules of M. The universal denominator behaves nicely with respect to short exact...

let $(r,m)$ be a commutative noetherian local ring, $m$ a finitely generated $r$-module of dimension $d$, and let $i$ be an ideal of definition for $m$. in this paper, we extend cite[corollary 10(4)]{p} and also we show that if $m$ is a cohen-macaulay $r$-module and $d=2$, then $lambda(frac{widetilde{i^nm}}{jwidetilde{i^{n-1}m}})$ does not depend on $j$ for all $ngeq 1$, where $j$ is a minimal ...

In this paper, we find explicit solution to the operator equation $TXS^* -SX^*T^*=A$ in the general setting of the adjointable operators between Hilbert $C^*$-modules, when $T,S$ have closed ranges and $S$ is a self adjoint operator.

The Hilbert series of the Garsia-Haiman module can be written as a generating function of standard fillings of Ferrers diagrams. It is conjectured by Haglund and Loehr that the Hilbert series of the diagonal harmonics can be written as a generating function of parking functions. In this paper we present a weight-preserving injection from standard fillings to parking functions for certain cases....

We will show that Feichtinger’s algebra S0(R ) (also known as modulation space M 0 (R ) and well defined for general locally compact Abelian groups) is a natural Hilbert module for quantum tori and that a result by V. Losert can be interpreted as implying that the construction of such Hilbert modules gives Feichtinger’s algebra, if one considers the category of time-frequency invariant homogeno...

The aim of this paper is to present a unified framework in the setting Hilbert $$C^*$$ -modules for scalar- and vector-valued reproducing kernel spaces -valued spaces. We investigate conditionally negative definite kernels with values -algebra adjointable operators acting on -module. In addition, we show that there exists two-sided connection between positive -modules. Furthermore, explore some...