We address the question “when the local image of a map is well defined” and answer it in case of holomorphic map germs with target (C^2,0). We prove a criterion for holomorphic map germs (X,x)→(Y,y) to be locally open, solving a conjecture by Huckleberry in all dimensions.
In the present paper we extend the Riemann–Roch formalism to structure algebras of moment graphs. We introduce and study the Chern character and push-forwards for twisted fibrations of moment graphs. We prove an analogue of the Riemann–Roch theorem for moment graphs. As an application, we obtain the Riemann–Roch type theorem for the equivariant K‑theory of some Kac–Moody flag varieties.
Johannes SjöstrandInstitut de Mathématiques de Bourgogne, Université de Bourgogne Franche-Comté, Dijon, FranceMaher ZerzeriLaboratoire Analyse, Géométrie et Applications, Université Sorbonne Paris-Nord, Villetaneuse, France
Analysis of PDEsFunctional Analysismathscidoc:2203.03008
In this paper we study the distribution of scattering resonances for a multi-dimensional semi-classical Schrödinger operator, associated to a potential well in an island at energies close to the maximal one that limits the separation of the well and the surrounding sea.