Related papers: A residue current associated with a twisting cocha…

Cohesive module provides a tool to study coherent sheaves on complex manifolds by global analytic methods. In this paper we develop the theory of residue currents for cohesive modules on complex manifolds. In particular we prove that they…

Given two ideals $\mathcal{I}$ and $\mathcal{J}$ of holomorphic functions such that $\mathcal{I} \subseteq \mathcal{J}$, we describe a comparison formula relating the Andersson-Wulcan currents of $\mathcal{I}$ and $\mathcal{J}$. More…

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…

We give a factorization of the cycle of a bounded complex of vector bundles in terms of certain associated differential forms and residue currents. This is a generalization of previous results in the case when the complex is a locally free…

We construct Coleff-Herrera products and Bochner-Martinelli type residue currents associated with a tuple $f$ of weakly holomorphic functions, and show that these currents satisfy basic properties from the (strongly) holomorphic case, as…

We study residue currents of the Bochner--Martinelli type using their relationship with Mellin transforms of residue integrals. We present the structure formula for residue currents associated with monomial mappings: they admit…

We give a factorization of the fundamental cycle of an analytic space in terms of certain differential forms and residue currents associated with a locally free resolution of its structure sheaf. Our result can be seen as a generalization…

For a Cohen-Macaulay ideal of holomorphic functions, we construct by elementary means residue currents whose annihilator is precisely the given ideal. We give two proofs that the currents have the prescribed annihilator, one using the…

Let $\mathcal{F}$ be a coherent sheaf on a complex variety $X$ that has a locally free resolution $E^{\bullet}$. In [19], the authors constructed a pseudomeromorphic current whose support is contained in $supp(E^{\bullet})$ that represents…

We introduce a class of flat currents with fractal properties, called fractional currents, which satisfy a compactness theorem and remain stable under pushforwards by H\"older continuous maps. In top dimension, fractional currents are the…

We derive a semiclassical formula for the tunneling current of electrons trapped in a potential well which can tunnel into and across a wide quantum well. The calculations idealize an experimental situation where a strong magnetic field…

Given a coherent ideal sheaf $J$ we construct locally a vector-valued residue current $R$ whose annihilator is precisely the given sheaf. In case $J$ is a complete intersection, $R$ is just the classical Coleff-Herrera product. By means of…

Given an ideal $\mathcal{J}$ on a complex manifold, Andersson and Wulcan constructed a current $R^\mathcal{J}$ such that the annihilator of $R^\mathcal{J}$ is $\mathcal{J}$, generalizing the duality theorem for Coleff-Herrera products. We…

With a given holomorphic section of a Hermitian vector bundle, one can associate a residue current by means of Cauchy-Fantappi\`e-Leray type formulas. In this paper we define products of such residue currents. We prove that, in the case of…

Given a free resolution of an ideal $\mathfrak{a}$ of holomorphic functions, one can construct a vector-valued residue current, $R$, which coincides with the classical Coleff-Herrera product if $\mathfrak{a}$ is a complete intersection…

Several authors have introduced various type of coherent-like rings and proved analogous results on these rings. It appears that all these relative coherent rings and all the used techniques can be unified. In [2], several coherent-like…

We associate bicomplexes with the finite Toda lattice and with a finite Toda field theory in such a way that conserved currents and charges are obtained by a simple iterative construction.

We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence modules, and show that they contain equivalent…

We consider the continuity equation for open chaotic quantum systems in the semiclassical limit. First we explicitly calculate a semiclassical expansion for the probability current density using an expression based on classical…

We calculate exactly the Josephson current for $c$-axis coherent tunneling between two layered superconductors, each with internal coherent tight-binding intra- and interlayer quasiparticle dispersions. Our results also apply when one or…