Related papers: Basic finite \'etale equivalence relations

In this paper, we introduce quotients of \'etale groupoids. Using the notion of quotients, we describe the abelianizations of groupoid C*-algebras. As another application, we obtain a simple proof that effectiveness of an \'etale groupoid…

The goal of this article is to study results and examples concerning finitely presented covers of finitely generated amenable groups. We collect examples of groups $G$ with the following properties: (i) $G$ is finitely generated, (ii) $G$…

We consider fibrations by affine lines on smooth affine surfaces obtained as complements of smooth rational curves $B$ in smooth projective surfaces $X$ defined over an algebraically closed field of characteristic zero. We observe that…

We investigate properties of the Albanese map and the fundamental group of a complex projective variety with many rational points over some function field, and prove that every linear quotient of the fundamental group of such a variety is…

In this paper we prove a characterization of quotients of Abelian varieties by the actions of finite groups that are free in codimension-one via some vanishing conditions on the orbifold Chern classes. The characterization is given among a…

In this paper we describe the fundamental group-scheme of a proper variety fibered over an abelian variety with rationally connected fibers over an algebraically closed field. We use old and recent results for the Nori fundamental…

We carry out the classification of abelian Lie symmetry algebras of two-dimensional second-order nondegenerate quasilinear evolution equations. It is shown that such an equation is linearizable if it admits an abelian Lie symmetry algebra…

We classify essential algebras whose irredundant non-refinable covers consist of primal algebras. The proof is obtained by constructing one to one correspondence between such algebras and partial orders on finite sets. Further, we prove…

We study degenerations of non-simple principally polarized abelian surfaces to the boundary in the toroidal compactification of $\mathcal{A}_2$, and describe the degenerate abelian surfaces as well as the degenerate elliptic curves that…

We show that every finite Abelian algebra A from congruence-permutable varieties admits a full duality. In the process, we prove that A also allows a strong duality, and that the duality may be induced by a dualizing structure of finite…

We explicitly describe the Albanese morphism of a hyperelliptic variety, i.e., the quotient $X$ of an abelian variety $A$ by a finite group $G$ acting freely and not only by translations, by giving a description of the Albanese variety and…

We explicitly construct special Lagrangian fibrations on finite quotients of maximally degenerating abelian varieties, glue with Berkovich retraction in non-Archimedean geometry by using "hybrid" technique. We also study their symmetries…

We prove a linearization theorem for pre-rings of endogenies acting on a definable abelian group of finite dimension. Observe that no assumptions on the connectivity of A are made. We also prove a similar result when one of the two…

A great sphere fibration is a sphere bundle with total space $S^n$ and fibers which are great $k$-spheres. Given a smooth great sphere fibration, the central projection to any tangent hyperplane yields a \emph{nondegenerate} fibration of…

We study the behavior of irregular fibrations of a variety under derived equivalence of its bounded derived category. In particular we prove the derived invariance of the existence of an irregular fibration over a variety of general type,…

We classify elliptic fibrations birational to a nonsingular, minimal cubic surface over a field of characteristic zero. Our proof is adapted to provide computational techniques for the analysis of such fibrations, and we describe an…

In this manuscript, we investigate regularity estimates for a class of quasilinear elliptic equations in the non-divergence form that may exhibit degenerate behavior at critical points of their gradient. The prototype equation under…

For each $n\ge2$ we classify all $n$-dimensional algebras over an arbitrary infinite field which have the property that the $n$-dimensional abelian Lie algebra is their only proper degeneration.

We prove that for an abelian group $G$ of order $n$ the morphism $ \varphi\colon \mathbf{P}(V^*)\longrightarrow \mathbf{P} ((\mathrm{sym}^n V^*)^G)$ defined by $\varphi([f]) = [\prod_{\sigma\in G} \sigma \cdot f ]$ is nondegenerate for…

We show that a minimal ideal of a finite-dimensional Lie algebra is either simple or abelian.