Related papers: Some remarks on flatness of morphisms over smooth …
We prove an improvement of flatness result for nonlocal minimal surfaces which is independent of the fractional parameter $s$ when $s\rightarrow 1^-$. As a consequence, we obtain that all the nonlocal minimal cones are flat and that all the…
It is known that spherically symmetric spacetimes admit flat spacelike foliations. We point out a simple method of seeing this result via the Hamiltonian constraints of general relativity. The method yields explicit formulas for the…
In this paper we introduce flat grafting as a deformation of quadratic differentials on a surface of finite type that is analogous to the grafting map on hyperbolic surfaces. Flat grafting maps are generic in the strata structure and…
In this paper we will study the representations of isomorphisms between bases of topological spaces. It turns out that the perfect setting for this study is that of regular open subsets of complete metric spaces, but we have achieved some…
In this paper we present a systematic study of the reflexivity properties of homologically finite complexes with respect to semidualizing complexes in the setting of nonlocal rings. One primary focus is the descent of these properties over…
We investigate the relation between partial silting modules, Gabriel topologies, and ring epimorphisms, with a particular emphasis on commutative rings. We show that a ring epimorphism of commutative rings is flat if and only if it is a…
We give a short proof that any smooth (means formally smooth and finitely presented) homomorphism of rings can be obtained by base change from a smooth homomorphism of noetherian rings. Together with the elegant short proof by J. Conde-Lago…
It is classically known that complete flat surfaces in Euclidean 3-space are cylinders over space curves. This implies that the study of global behaviour of flat surfaces requires the study of singular points as well. If a flat surface $f$…
With a simple generic approach, we develop a classification that encodes and measures the strength of completeness (or compactness) properties in various types of spaces and ordered structures. The approach also allows us to encode notions…
We study moduli of semistable twisted sheaves on smooth proper morphisms of algebraic spaces. In the case of a relative curve or surface, we prove results on the structure of these spaces. For curves, they are essentially isomorphic to…
In this paper we introduce the notion of almost flatness for (stably) relative bundles on a pair of topological spaces and investigate basic properties of it. First, we show that almost flatness of topological and smooth sense are…
Our work aims to introduce generalization of soft $ \mu $-compact soft generalized topological spaces, namely; soft nearly $ \mu $-compact spaces which are defined over initial universe with a fixed set of parameters. Basic properties and…
Let $K$ be a field of characteristic zero, $X$ and $Y$ be smooth $K$-varieties, and let $G$ be a algebraic $K$-group. Given two algebraic morphisms $\varphi:X\rightarrow G$ and $\psi:Y\rightarrow G$, we define their convolution…
Motivated by applications in moduli theory, we introduce a flexible and powerful language for expressing lower bounds on relative dimension of morphisms of schemes, and more generally of algebraic stacks. We show that the theory is robust…
The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set. Sambin's notion of an overlap algebra, although…
Given a relatively minimal non locally trivial fibred surface f: S->B, the slope of the fibration is a numerical invariant associated to the fibration. In this paper we explore how properties of the general fibre of $f$ and global…
One of the questions investigated in deformation theory is to determine to which algebras can a given associative algebra be deformed. In this paper we investigate a different but related question, namely: for a given associative…
Classically, regular homomorphisms have been defined as a replacement for Abel--Jacobi maps for smooth varieties over an algebraically closed field. In this work, we interpret regular homomorphisms as morphisms from the functor of families…
Let $X$ and $S$ be complex spaces with $X$ countable at infinity and $S$ reduced locally pure dimensional. Let $\pi:X\to S$ be an universally-$n$-equidimensional morphism (i.e open with constant pure $n$-dimensional fibers). If there is a…
Let $\Sigma$ be a closed surface, $G$ a compact Lie group, with Lie algebra $g$, $\xi \colon P \to \Sigma$ a principal $G$-bundle, let $N(\xi)$ denote the moduli space of central Yang-Mills connections on $\xi$, for suitably chosen…