Related papers: Irregular fibers of complex polynomials in two var…
We introduce the notion of locally consistent system of half-spaces for a real hyperplane arrangement. We embed a sphere in the complexified complement by shifting the real unit sphere into the imaginary direction indicated by the…
In this article, we give two different sufficient conditions for the irreducibility of a polynomial of more than one variable, over the field of complex numbers, that can be written as a sum of two polynomials which depend on mutually…
A morphism of a category which is simultaneously an epimorphism and a monomorphism is called a bimorphism. In \cite{DR2} we gave characterizations of monomorphisms (resp. epimorphisms) in arbitrary pro-categories, pro-(C), where (C) has…
We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…
A module is called automorphism-invariant if it is invariant under any automorphism of its injective envelope. In this survey article we present the current state of art dealing with such class of modules.
We consider principal fibre bundles with a given connection and construct almost complex structures on the total space if the adjoint bundle is isomorphic to the tangent bundle of the base. We derive the integrability condition. If the…
We prove that a quasi-finite endomorphism of an algebraic variety over an algebraically closed field of characteristic zero, that is injective on the complement of a closed subvariety, is an automorphism. We also prove that an endomorphism…
It is shown that in dimension at least three a local diffeomorphism of Euclidean n-space into itself is injective provided that the pull-back of every plane is a Riemannian submanifold which is conformal to a plane. Using a similar…
We want to compute generic $\mathrm{Ext}$-spaces of twisted polynomial functors in relation to the $\mathrm{Ext}$-spaces of the untwisted ones, modulo a parametrisation. Thanks to the study of a spectral sequence we get to a computation in…
For a field $E$ of characteristic different from $2$ and cohomological $2$-dimension one, quadratic forms over the rational function field $E(X)$ are studied. A characterisation in terms of polynomials in $E[X]$ is obtained for having that…
In principle, Floer theory can be extended to define homotopy invariants of families of equivalent objects (e.g. Hamiltonian isotopic symplectomorphisms, 3-manifolds, Legendrian knots, etc.) parametrized by a smooth manifold B. The…
A system of commutative hyperbolic complex numbers in 2 dimensions is studied in this paper. Exponential and trigonometric forms are obtained for these hyperbolic twocomplex numbers. Expressions are given for the elementary functions of…
Given two nilpotent endomorphisms, we determine when their lattices of hyperinvariant subspaces are isomorphic. The study of the lattice of hyperinvariant subspaces can be reduced to the nilpotent case when the endomorphism has a…
An important invariant of a polynomial $f$ is its Jacobian algebra defined by its partial derivatives. Let $f$ be invariant with respect to the action of a finite group of diagonal symmetries $G$. We axiomatically define an orbifold…
New invariants for 2-dimensional cell complexes are defined, which can be interpreted as curvature bounds. These invariants are proved to be rational and computable in a companion article. This document is a survey that collects theorems…
We characterize possible periodic subvarieties for surjective endomorphisms of complex abelian varieties in terms of the eigenvalues of the cohomological actions induced by the endomorphisms, extending previous work in this direction by…
We give a topological model for a polynomial map from $\C^n$ to $\C$ in the neighborhood of a fiber with isolated singularities. This is motivated out of the ``unfolding of links'' described earlier by the first author and Lee Rudolph. The…
Let $f\colon X\to\mathbb{A}^1_k$ be a morphism from a smooth variety to an affine line with an isolated singular point. For such a singularity, we have two invariants. One is a non-degenerate symmetric bilinear form (de Rham), and the other…
Based on the recent developments in the irregular Riemann-Hilbert correspondence for holonomic D-modules and the Fourier-Sato transforms for enhanced ind-sheaves, we study the Fourier transforms of some irregular holonomic D-modules. For…
Given a family $X$ of complex varieties degenerating over a punctured disc, one is interested in computing related invariants called the motivic nearby fiber and the refined limit mixed Hodge numbers, both of which contain information about…