Related papers: Completeness and compactness for varieties over lo…

Let $K=k(C)$ be the function field of a smooth projective curve $C$ over an infinite field $k$, let $X$ be a projective variety over $k$. We prove two results. First, we show with some conditions that a $K$-morphism $\phi: X_K \to X_K$ of…

Let $X$ be a quasi-affine algebraic variety isomorphic to the complement of a closed subvariety of dimension at most $n-3$ in $\C^n$. We find some conditions under which an isomorphism of two closed subvarieties of $X$ can be extended to an…

Duality for complete discrete valuation fields with perfect residue field with coefficients in (possibly p-torsion) finite flat group schemes was obtained by Begueri, Bester and Kato. In this paper, we give another formulation and proof of…

In this paper, we study the properties of coverings of locally conformally K\"ahler (LCK) spaces with singularities. We begin by proving that a space is LCK if any only if its universal cover is K\"ahler, thereby generalizing a result from…

A generalized topology in a set $X$ is a collection $\text{Cov}_X$ of families of subsets of $X$ such that the triple $(X,\bigcup \text{Cov}_X,\text{Cov}_X)$ is a generalized topological space in the sense of Delfs and Knebusch. In this…

Some new classes of compacta $K$ are considered for which $C(K)$ endowed with the pointwise topology has a countable cover by sets of small local norm--diameter.

We prove that Keimel and Lawson's K-completion Kc of the simple valuation monad Vs defines a monad Kc o Vs on each K-category A. We also characterize the Eilenberg-Moore algebras of Kc o Vs as the weakly locally convex K-cones, and its…

We prove the following theorem for Holomorphic Foliations in compact complex kaehler manifolds: if there is a compact leaf with finite holonomy, then every leaf is compact with finite holonomy. As corollary we reobtain stability theorems…

A graph is called $k$-extendable if each $k$-matching can be extended to a perfect matching. We give spectral conditions for the $k$-extendability of graphs and bipartite graphs using Tutte-type and Hall-type structural characterizations.…

Let $X$ be a scheme over a field $K$ and let $M_X$ be the intersection of all subfields $L$ of $\bar K$ such that $X$ has a $L$-valued point. In this note we prove that for a variety $X$ over a field $K$ finitely generated over its prime…

Let $X$ be a space. A space $Y$ is called an extension of $X$ if $Y$ contains $X$ as a dense subspace. For an extension $Y$ of $X$ the subspace $Y\backslash X$ of $Y$ is called the remainder of $Y$. Two extensions of $X$ are said to be…

Any unital separable continuous C(X)-algebra with properly infinite fibres is properly infinite as soon as the compact Hausdorff space X has finite topolog-ical dimension. We study conditions under which this is still the case if the…

We prove that if $K$ is a compact subset of an affine variety O = P^n - D (where D is a projective hypersuface), and if K is a compact subset of a closed analytic subvariety V \subset O, then the projective hull K^ of K has the property…

Given a finite field k of characteristic at least 5, we show that the Tate conjecture holds for K3 surfaces defined over the algebraic closure of k if and only if there are only finitely many K3 surfaces over each finite extension of k.

In this note we introduce the concept of a quasi-finite complex. Next, we show that for a given countable and locally finite CW complex L the following conditions are equivalent: (i) L is quasi-finite. (ii) There exists a [L]-invertible…

We study properties of the Golomb topology on polynomial rings over fields, in particular trying to determine conditions under which two such spaces are not homeomorphic. We show that if $K$ is an algebraic extension of a finite field and…

Let X be a geometrically rational (or more generally, separably rationally connected) variety over a finite field K. We prove that if K is large enough then X contains many rational curves defined over K. As a consequence we prove that…

The complexity of a pair $(X,B)$ is an invariant that relates the dimension of $X$, the rank of the group of divisors, and the coefficients of $B$. If the complexity is less than one, then $X$ is a toric variety. We prove that if the…

A space has $\sigma$-compact tightness if the closures of $\sigma$-compact subsets determines the topology. We consider a dense set variant that we call densely k-separable. We consider the question of whether every densely k-separable…

Let $\mathbb{K}$ be a discrete field and $(V, \phi)$ a flow over the category of locally linearly compact $\mathbb{K}$-spaces. Here we give the formulas to compute the topological entropy of $(V,\phi)$ subject to the extension or the…