Related papers: Non-uniformly flat affine algebraic hypersurfaces

In this paper we study the affine focal set, which is the bifurcation set of the affine distance to submanifolds $N^n$ contained in hypersurfaces $M^{n+1}$ of the $(n+2)$-space. We give condition under which this affine focal set is a…

We prove that the space of affine, transversal at infinity, non-singular real cubic surfaces has 15 connected components. We give a topological criterion to distinguish them and show also how these 15 components are adjacent to each other…

This paper is concerned with two generalizations of the Hopf algebra of symmetric functions that have more or less recently appeared. The Hopf algebra of noncommutative symmetric functions and its dual, the Hopf algebra of quasisymmetric…

We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.

In the framework of light-cone gauge formulation, massless arbitrary spin N=1 supermultiplets in four-dimensional flat space are considered. We study both the integer (super)spin and half-integer (super)spin supermultiplets. For such…

We identify a class of smooth Banach *-algebras that are differential subalgebras of commutative C*-algebras whose openness of multiplication is completely determined by the topological stable rank of the target C*-algebra. We then show…

Cubic surfaces in characteristic two are investigated from the point of view of prime characteristic commutative algebra. In particular, we prove that, the non-Frobenius split cubic surfaces form a linear subspace of codimension four in the…

We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in…

We compute the differential geometric invariants of cuspidal edges on flat surfaces in hyperbolic $3$-space and in de Sitter space. Several dualities of invariants are pointed out.

Let {(Z_i,W_i):i=1,...,n} be uniformly distributed in [0,1]^d * G(k,d), where G(k,d) denotes the space of k-dimensional linear subspaces of R^d. For a differentiable function f from [0,1]^k to [0,1]^d we say that f interpolates (z,w) in…

A continous map $f: \mathbb{C}^n \rightarrow \mathbb{C}^N$ is $k$-regular if the image of any $k$ points spans a $k$-dimensional subspace. It is an important problem in topology and interpolation theory, going back to Borsuk and Chebyshev,…

We extend our work on nonseparated interpolating sequences, originally developed for Bergman spaces with weights of the form $(1 - |z|^2)^\alpha$, to more general weights.

The Russell cubic is a smooth contractible affine complex threefold which is not isomorphic to affine three-space. In previous articles, we discussed the structure of the automorphism group of this variety. Here we review some consequences…

Let $(M,g)$ be a smooth connected Riemannian manifold. We show an improvement of flatness theorem for hypersurfaces of $M$ of bounded nonlocal mean curvature in the viscosity sense. It implies local $ C^{1,\alpha}$ regularity of these…

We derive a sharp inequality relating the second and fourth elementary symmetric functions of the eigenvalues of a trace-free matrix and give two applications. First, we give a new proof of the classification of conformally flat…

We remark some basic facts on homological aspects of involutive Lie bialgebras and their involutive bimodules, and present some problems on surface topology related to these facts.

We consider the problem of interpolating projective varieties through points and linear spaces. We show that del Pezzo surfaces satisfy weak interpolation.

We study complements of hypersurfaces in schemes with respect to the property being affine.

We present two classes of examples of Hopf algebroids associated with noncommutative principal bundles. The first comes from deforming the principal bundle while leaving unchanged the structure Hopf algebra. The second is related to…

A topological hyperplane is a subspace of R^n (or a homeomorph of it) that is topologically equivalent to an ordinary straight hyperplane. An arrangement of topological hyperplanes in R^n is a finite set H such that k topological…