Related papers: On dicritical singularities of Levi-flat sets
The purpose of this paper is to generalize in a geometric setting theorems of Severi, Brown and Bochner about analytic continuation of real analytic functions which are holomorphic or harmonic with respect to one of its variables. We prove…
Consider a Leibniz superalgebra $\mathfrak L$ additionally graded by an arbitrary set $I$ (set grading). We show that $\mathfrak L$ decomposes as the sum of well-described graded ideals plus (maybe) a suitable linear subspace. In the case…
We prove a "strong" Durfee-type inequality for isolated hypersurface surface singularities, which implies Durfee's strong conjecture for such singularities with non-negative topological Euler number of the exceptional set of the minimal…
Linearly repetitive Delone sets are shown to be rectifiable by a bi-Lipschitz homeomorphisms of the Euclidean space that sends the Delone set to the set of points with integer coordinates.
A general ansatz in Renormalization Theory, already established in many important situations, states that exponential convergence of renormalization orbits implies that topological conjugacies are actually smooth (when restricted to the…
Iterated Segre mappings of real analytic generic submanifolds in complex space have been an essential tool in the study of holomorphic, formal, and CR mappings between such manifolds. In this paper we present a theory of iterated Segre…
Decomposition classes provide a way of partitioning the Lie algebras of an algebraic group into equivalence classes based on the Jordan decomposition. In this paper, we investigate the decomposition classes of the Lie algebras of connected…
We show that for multi-colored Delone point sets with finite local complexity and uniform cluster frequencies the notions of pure point diffraction and pure point dynamical spectrum are equivalent.
We consider functions with isolated critical points on a closed surface. We prove that in a neighborhood of a critical point the function conjugates with Re$z^k$ for the some nonnegative integer k. The full topological invariant of such…
We study the minimizer u of a convex functional in the plane which is not G\^ateaux-differentiable. Namely, we show that the set of critical points of any C^1-smooth minimizer can not have isolated points. Also, by means of some appropriate…
We prove a Diophantine approximation inequality for closed subschemes on surfaces which can be viewed as a joint generalization of recent inequalities of Ru-Vojta and Heier-Levin in this context. As applications, we study various…
A connected real analytic hypersurface M in C^(n+1) whose Levi form is nondegenerate in at least one point - hence at every point of some Zariski-open subset - is locally biholomorphic to the model Heisenberg quadric pseudosphere of…
This paper investigates Levi flat structures from the perspective of structure sheaves. We employ formal integrability to construct a class of differential complexes, thereby providing a resolution for the structure sheaf and a global…
A generalization of the Auslander conjecture is proved in the case when the Levi factor of the Zariski closure of the acting group is a product of simple real algebraic groups of rank \leq 1. Also, the Auslander conjecture is proved for…
In this paper we classify degenerate Verma modules over the linearly compact Lie superalgebra $E(4,4)$. This completes the description of Verma modules over the exceptional linearly compact Lie superalgebras. As in the other cases all…
An explicit realization of the affine Lie algebra \hat{sl}_2(C) at the critical level is constructed using a mixture of bosons and parafermions. Subsequently a representation of the associated Lepowsky-Wilson Z-algebra is given on a space…
The author has previously shown that solvable Lie A-algebras and complemented solvable Lie algebras decompose as a vector space direct sum of abelian subalgebras, and their ideals relate nicely to this decomposition. However, neither of…
We develop the notions of connections and curvature for general Lie-Rinehart algebras without using smoothness assumptions on the base space. We present situations when a connection exists. E.g., this is the case when the underlying module…
The first part of this paper considers higher order CR invariants of three dimensional hypersurfaces of finite type. Using a full normal form we give a complete characterization of hypersurfaces with trivial local automorphism group, and…
The fixed point variety of a regular unipotent element on a wonderful completion is investigated. For the wonderful completion of the quotient by a symmetric Levi subgroup, it is shown that the fixed point variety is $SL_2$-regular.