Related papers: Decomposition of residue currents

We study the behavior of Stanley decompositions and of pretty clean filtrations under reduction modulo a regular element.

We calculate the decomposition series of the D-module defined as the push-forward of a rank one linear system on the complement of a normal crossings hyperplane configuration and use data of a resolution of singularities to give a…

We present research on radiative decays of vector ($J^{PC}=1^{--}$) to pseudoscalar ($J^{PC}=0^{-+}$) particles ($u$, $d$, $s$, $c$, $b$, $t$ quark system) using broken symmetry techniques in the infinite momentum frame and equal time…

Primary decomposition is a very important tool of commutative algebra and geometry. In this paper we generalized some of the existing algorithms of primary decomposition developed by Eisenbud et al. (cf. [EHV]) for free modules and also…

In the persistent homology of filtrations, the indecomposable decompositions provide the persistence diagrams. However, in almost all cases of multidimensional persistence, the classification of all indecomposable modules is known to be a…

Let $\mathfrak a$ be an ideal of a commutative Noetherian ring $R$ and $t$ be a non-negative integer. Let $M$ and $N$ be two finitely generated $R$-modules. In certain cases, we give some bounds under inclusion for the annihilators of…

Using Bochner-Martinelli type residual currents we prove some generalizations of Jacobi's Residue Formula, which allow proper polynomial maps to have `common zeroes at infinity', in projective or toric situations.

The deformed current Lie algebra was introduced by the author to study the representation theory of cyclotomic q-Schur algebras at q=1. In this paper, we classify finite dimensional simple modules of deformed current Lie algebras.

This work describes a powerful, yet simple, procedure how to acquire a current approaching the lower bound of quality factor Q. This optimal current can be determined for an arbitrarily shaped electrically small radiator made of a perfect…

We give a local criterion in terms of a residue current for strong holomorphicity of a meromorphic function on an arbitrary pure-dimensional analytic variety. This generalizes a result by A Tsikh for the case of a reduced complete…

Consider an ideal $I \subset R = \bC[x_1,...,x_n]$ defining a complex affine variety $X \subset \bC^n$. We describe the components associated to $I$ by means of {\em numerical primary decomposition} (NPD). The method is based on the…

We develop JSJ decomposition theory of pro-p groups.

We find canonical decompositions for finitely presented groups which specialize to the classical JSJ-decomposition when restricted to the fundamental groups of Haken manifolds. The decompositions that we obtain are invariant under…

We show that Coleff-Herrera type products of residue currents can be defined by analytic continuation of natural functions depending on one complex variable.

Let A be a complete discrete valuation ring with possibly imperfect residue field. The purpose of this paper is to give a notion of conductor for Galois representations over A that generalizes the classical Artin conductor. The definition…

We consider nonnegative r-potent matrices with finite dimensions and study their decomposability. We derive the precise conditions under which an r-potent matrix is decomposable. We further determine a general structure for the r-potent…

Let $\mathcal{F}$ be a coherent $\mathcal{O}_X$-module over a complex manifold $X$, and let $G$ be a vector bundle on $X$. We describe an explicit isomorphism between two different representations of the global…

In this paper screening currents of the second kind are considered. They are constructed in any affine current algebra for directions corresponding to simple roots with multiplicity one in a decomposition of the highest root on a set of…

The critical currents in Josephson junctions of conventional superconductors with macroscopic defects are calculated for different defect critical current densities as a function of the magnetic field. We also study the evolution of the…

We study the decomposability and the subdifferential of the tensor nuclear norm. Both concepts are well understood and widely applied in matrices but remain unclear for higher-order tensors. We show that the tensor nuclear norm admits a…