Related papers: A note on dual abelian varieties

It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most $3$ separate the orbits. A result providing an upper degree bound for separating…

Using properties of the Frobenius eigenvalues, we show that, in a precise sense, ``most'' isomorphism classes of (principally polarized) simple abelian varieties over a finite field are characterized up to isogeny by the sequence of their…

We consider the structures formed by isogenies of abelian varieties with polarizations that are not necessarily principal, specifically with the $[\ell]$-polarizations we have previously defined. Our primary interest is in superspecial…

In this short note we study the questions of (non-)L-equivalence of algebraic varieties, in particular, for abelian varieties and K3 surfaces. We disprove the original version of a conjecture of Huybrechts \cite[Conjecture 0.3]{H} stating…

We give an explicit formula for the Mordell-Weil rank of an abelian fibered variety and some of its applications for an abelian fibered hyperk\"ahler manifold. As a byproduct, we also give an explicit example of an abelian fibered variety…

Let $A$ be an abelian variety in a field of characteristic $0$. We prove that the expansion of $A$ by a generic divisible subgroup of $A$ with the same torsion exists provided $A$ has few algebraic endomorphisms, namely…

The results in this paper imply that for every number field F and positive integer r, there exists an F-isogeny class of abelian varieties such that r divides the degree of every F-polarization on every abelian variety in the isogeny class.

We extend the loop algebra construction for algebras graded by abelian groups to study graded-simple algebras over the field of real numbers (or any real closed field). As an application, we classify up to isomorphism the graded-simple…

In this note we prove that a smooth projective variety (defined over a field $k$) of non-negative Kodaira dimension that has a $k$-rational point and a polarized self map must be a finite free quotient of an abelian variety.

The strata of the moduli spaces of Abelian differentials are non-homogenous spaces carrying natural bi-algebraic structures. Partly inspired by the case of homogenous spaces carrying bi-algebraic structures (such as torii, Abelian varieties…

A class of two-dimensional globally scale-invariant, but not conformally invariant, theories is obtained. These systems are identified in the process of discussing global and local scaling properties of models related by duality…

For fixed $k<g$ and a family of polarized abelian varieties of dimension $g$ over $\mathbb{R}$, we give a criterion for the density in the parameter space of those abelian varieties over $\mathbb{R}$ containing a $k$-dimensional abelian…

There are several examples in the literature of finite non-abelian $p$-groups whose automorphism group is abelian. For some time only examples that were special $p$-groups were known, until Jain and Yadav [JY12] and Jain, Rai and Yadav…

The standard notion of the non-Abelian duality in string theory is generalized to the class of $\si$-models admitting `non-commutative conserved charges'. Such $\si$-models can be associated with every Lie bialgebra $(\cg ,\cgt)$ and they…

The work is devoted to the variety of $2$-dimensional algebras over an algebraically closed field. Firstly, we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of principal algebra series in the…

In this article we construct for each integer $n\ge 2$ an abelian variety $A$ of dimension $n$ defined over a number field for which there exists a symmetric slope sequence of length $2n$ that does not appear as the slope sequence of…

In this paper, we present complete classifications, up to isomorphism, of all two-element dimonoids, all commutative three-element dimonoids, and all abelian three-element dimonoids. We show that, up to isomorphism, there exist exactly 8…

We discuss the conditions under which non-abelian T-duality can be considered as a chain of abelian T-dualities. Motivated by these results, we propose that the topology of a non-abelian T-dual should be phrased in the language of T-folds,…

In this paper, we study the theory of non-abelian extensions of a Leibniz conformal algebra $R$ by a Leibniz conformal algebra $H$ and prove that all the non-abelian extensions are classified by non-abelian $2$nd cohomology $H^2_{nab}(R,H)$…

We construct 3-manifolds which have at least two inequivalent embeddings such that both complementary regions have abelian fundamental group.