Related papers: Non-vanishing forms in projective space over finit…

Simple constructions are given for finite semifields that include as special cases both old semifields and recently constructed semifields.

For a finite vector space $V$ and a non-negative integer $r\le\dim V$ we estimate the smallest possible size of a subset of $V$, containing a translate of every $r$-dimensional subspace. In particular, we show that if $K\subset V$ is the…

This is a detailed study of the infinitesimal variation of the variety of lines through a point of a low degree hypersurface in pro jective space. The motion is governed by a system of partial differential equations which we describe…

We study sets of finite perimeter in Wiener space, and prove that at almost every point (with respect to the perimeter measure) a set of finite perimeter blows-up to a halfspace.

We give a lower bound for the degree of a finite cover of a hyperbolic 3-manifold which fibers over the circle, in terms of volume, the diameter of the manifold and other new invariants.

In the first part of this article, we consider ruled surfaces defined over a finite field; we introduce invariants for them, and describe some explicit contructions that illustrate possible behaviour of these invariants. In the second part,…

We consider random fields that can be represented as integrals of deterministic functions with respect to infinitely divisible random measures and show that these random fields are infinitely divisible.

The article is devoted to the investigation of particular classes of quasi-invariant descending at infinity measures on linear spaces over non-Archimedean fields such that measures are with values in non-Archimedean fields also. Their…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

The main purpose of this note is to establish the continuity of seminorms on finite-dimensional vector spaces over the real or complex numbers.

We endow the set of complements of a fixed subspace of a projective space with the structure of an affine space, and show that certain lines of such an affine space are affine reguli or cones over affine reguli. Moreover, we apply our…

We bound the genus of a projective curve lying on a complete intersection surface in terms of its degree and the degrees of the defining equations of the surface on which it lies.

Consider a finite morphism f:X -> Y of smooth projective varieties over a finite field k. Suppose X is the vanishing locus in projective N-space of at most r forms of degree at most d. We show there is a constant C, depending only on N, r,…

We give upper and lower bounds on the number of points on abelian varieties over finite fields, and lower bounds specific to Jacobian varieties. We also determine exact formulas for the maximum and minimum number of points on Jacobian…

We provide formulas for projectors onto a polyhedral set, i.e. the intersection of a finite number of halfspaces. To this aim we formulate the problem of finding the projection as a convex optimization problem and we solve explicitly…

Let (X,d) be a finite metric space. This paper first discusses the spectrum of the p-distance matrix of a finite metric space of p-negative type and then gives upper and lower bounds for the so called gap of a finite metric space of strict…

We address several extremal problems concerning the spreading property of point sets of Steiner triple systems. This property is closely related to the structure of subsystems, as a set is spreading if and only if there is no proper…

We prove the existence of global minimal models for rational morphisms $\phi:{\mathbb P}^N\rightarrow{\mathbb P}^N$ of projective space defined over the field of fractions of a principal ideal domain.

We prove that every complete non-compact manifold of finite volume contains a (possibly non-compact) minimal hypersurface of finite volume. The main tool is the following result of independent interest: if a region $U$ can be swept out by a…

This paper offers an adaptation to the convenient setting of finite dimensional Nambu-Poisson structures. In particular, for partial Nambu structures, we look for those whose classical geometrical results in finite dimension can be extended…