Related papers: Segre nondegenerate totally real subvarieties

An involution $#$ on an associative ring $R$ is \textit{formally real} if a sum of nonzero elements of the form $r^# r$ where $r \in R$ is nonzero. Suppose that $R$ is a central simple algebra (i.e. $R=M_n(D)$ for some integer $n$ and…

In this paper, having introduced a convergence of a series on the root vectors in the Abel-Lidskii sense, we present a valuable application to the evolution equations. The main issue of the paper is an approach allowing us to principally…

Towards the Lang--Vojta conjecture, we prove results on finiteness and Zariski degeneracy of $S$-integral points of varieties over number fields $k$, including many cases with geometrically irreducible boundary divisors. Our approach builds…

We discuss the deformed sigma-model that arises when considering four-dimensional N=2 abelian vector multiplets in the presence of an arbitrary chiral background field. In addition, we allow for a class of deformations of special geometry…

In this work we study the space of derivations of non-degenerate evolution algebras. We improve some results obtained recently in the literature and, as a consequence, we advance in the description of the derivations for $n$-dimensional…

We study Veronese and Segre morphisms between non-commutative projective spaces. We compute finite reduced Gr\"obner bases for their kernels, and we compare them with their analogues in the commutative case.

We study equisingular deformation problems for curves and surfaces in algebraic families, with particular emphasis on situations where nodal behavior is no longer generic. Extending classical Severi theory, we develop deformation--theoretic…

A polar hypersurface P of a complex analytic hypersurface germ, f=0, can be investigated by analyzing the invariance of certain Newton polyhedra associated to the image of P, with respect to suitable coordinates, by certain morphisms…

Let $M \subset {\mathbb{C}}^{n+1}$, $n \geq 2$, be a real codimension two CR singular real-analytic submanifold that is nondegenerate and holomorphically flat. We prove that every real-analytic function on $M$ that is CR outside the CR…

A class of the Newell-Whitehead-Segel equations (also known as generalized Fisher equations and Newell-Whitehead equations) is studied with Lie and "nonclassical" symmetry points of view. The classifications of Lie reduction operators and…

We obtaine the full characterization of proper closed invariant subspaces of a generalized backward shift operator (Pommiez operator) in the Frechet space of all holomorphic functions on a simply connected domain $\Omega$ of the complex…

We introduce a class of uniformly $2$-nondegenerate CR hypersurfaces in $\mathbb{C}^N$, for $N>3$, having a rank $1$ Levi kernel. The class is first of all remarkable by the fact that for every $N>3$ it forms an {\em explicit}…

Motivated by the study of the secant variety of the Segre-Veronese variety we propose a general framework to analyze properties of the secant varieties of toric embeddings of affine spaces defined by simplicial complexes. We prove that…

We investigate the algebra and geometry of the independence conditions on discrete random variables in which we fix some random variables and study the complete independence of some subcollections. We interpret such independence conditions…

We study the linear algebra of finite subsets $S$ of a Segre variety $X$. In particular we classify the pairs $(S,X)$ with $S$ linear dependent and $\#(S)\le 5$. We consider an additional condition for linear dependent sets (no two of their…

Real-analytic Levi-flat codimension two CR singular submanifolds are a natural generalization to ${\mathbb{C}}^m$, $m > 2$, of Bishop surfaces in ${\mathbb{C}}^2$. Such submanifolds for example arise as zero sets of mixed-holomorphic…

In this paper we construct a large class of new normal forms for Levi-nondegenerate real hypersurfaces in complex spaces. We adopt a general approach illustrating why these normal forms are natural and which role is played by the celebrated…

Let $T$ be an absolutely continuous polynomially bounded operator, and let $\theta$ be a singular inner function. It is shown that if $\theta(T)$ is invertible and some additional conditions are fulfilled, then $T$ has nontrivial…

We examine two nonselfadjoint operator algebras: the weighted shift algebra, and the Volterra operator algebra. In both cases, the operator algebra is the norm closure of the polynomials in the operator norm. In the case of the weighted…

We study geometric properties of varieties associated with invariant subspaces of nilpotent operators. There are reductive algebraic groups acting on these varieties. We give dimensions of orbits of these actions. Moreover, a combinatorial…