Related papers: Engel theorem through singularities

In this paper, we show how to apply a theorem by L\^e D.T. and the author about linear families of curves on normal surface singularities to get new results in this area. The main concept used is a specific definition of {\em general…

Arnol'd showed the uniqueness of the complex analytic structure of a small neighborhood of a non-singular elliptic curve embedded in a non-singular surface whose normal bundle satisfies Diophantine condition in the Picard variety. We show…

We prove the Cartan-Eilenberg stable elements theorem and construct a Lyndon-Hochschild-Serre type spectral sequence for pro-fusion systems. As an application, we determine the continuous mod-$p$ cohomology ring of…

Homology with values in a connection with possibly irregular singular points on an algebraic curve is defined, generalizing homology with values in the underlying local system for a connection with regular singular points. Integration…

We prove Euler's theorem of number theory developing an argument based on quandles. A quandle is an algebraic structure whose axioms mimic the three Reidemeister moves of knot theory.

We prove a complexity dichotomy theorem for Holant Problems on 3-regular graphs with an arbitrary complex-valued edge function. Three new techniques are introduced: (1) higher dimensional iterations in interpolation; (2) Eigenvalue Shifted…

Hadwiger's theorem is a Helly-type theorem involving common transversals to families of convex sets instead of common intersections. Subsequently, Pollack and Wenger identified a necessary and sufficient condition, called a consistent…

Given a nonzero germ h of holomorphic function on (C^n,0), we study the condition: ``the ideal Ann\_D 1/h is generated by operators of order 1''. When h defines a generic arrangement of hypersurfaces with an isolated singularity, we show…

This paper is divided into two parts. The first is a review, through categorical lenses, of the classical theory of regular-singular differential systems over $C((x))$ and $\mathbb P^1_C\smallsetminus\{0,\infty\}$, where $C$ is…

We establish a general uniqueness theorem for subharmonic functions of several variables on a domain. A corollary from this uniqueness theorem for holomorphic functions is formulated in terms of the zero subset of holomorphic functions and…

We prove the existence of normal forms for some local real-analytic Levi-flat hypersurfaces with an isolated line singularity. We also give sufficient conditions for that a Levi-flat hypersurface with a complex line as singularity to be a…

We are interested in characterizing the holonomy maps associated to integral curves of non-degenerate singularities of holomorphic vector fields. Such a description is well-known in dimension 2 where is a key ingredient in the study of…

H. Hertz called any manifold M with a given nonintegrable distribution {\it nonholonomic}. Vershik and Gershkovich stated and R. Montgomery proved that the space of germs of any nonholonomic distribution on M with an open and dense orbit of…

Given an ample Hausdorff groupoid $G$, a unital commutative ring $R$, and a discrete twist $(\Sigma,i,q)$, we establish a generalised uniqueness theorem for the twisted Steinberg algebra $A_R(G;\Sigma)$. By applying this theorem when $G$ is…

We give several generalizations of Rellich's classical uniqueness theorem to unbounded domains. We give a natural half-space generalization for super-exponentially decaying inhomogeneities using real variable techniques. We also prove under…

In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.

Employing Morse theory for the global control of monodromy and the method of analytic discs for local extension, we establish a version of the global Hartogs extension theorem in a singular setting: for every domain D of an (n-1)-complete…

This paper improves some results of the author's previous work. We will investigate the case of non-smooth points on an automorphic components and prove Breuil-Schenider conjecture. As a consequence we will see that in case when all the…

There is a well known theorem by Deuring which gives a criterion for when the reduction of an elliptic curve with complex multiplication (CM) by the ring of integers of an imaginary quadratic field has ordinary or supersingular reduction.…

We prove an $L^2$ theorem on generically surjective morphism of holomorphic vector bundles via a degeneration argument, generalizing the author's previous work on the $L^2$ division theorem of Skoda. The proof is based on Berndtsson's…