Related papers: Sidon sets in algebraic geometry

A three-dimensional family of solutions of the Jacobi equations for Poisson systems is characterized. In spite of its general form it is possible the explicit and global determination of its main features, such as the symplectic structure…

We show that after mapping each element of a set of second class constraints to the surface of the other ones, half of them form a subset of abelian first class constraints. The explicit form of the map is obtained considering the most…

This paper is devoted to abelian varieties arising from generalized Legendre curves. In particular, we consider their corresponding Galois representations, periods, and endomorphism algebras. For certain one parameter families of…

We discuss Galois properties of points of prime order on an abelian variety that imply the simplicity of its endomorphism algebra. Applications to hyperelliptic jacobians are given. In particular, we improve some of our earlier results.

We construct the universal Mumford curve of given genus as a family of Mumford curves over the deformation space of degenerate curves in the category of arithmetic formal geometry. Furthermore, we give explicit formulas of abelian…

We study the set of Dedekind cuts over a linearly ordered Abelian group as a structure over the language (0,<,+,-). Moreover, we obtain a simple set of axioms for the universal part of the theory of such structures. Finally, we prove that…

We construct three families of pairs of genus 2 curves over a field K, whose Jacobians are isomorphic as unpolarized abelian varieties. Each family is parameterized by an open subset of the Projective line over K. Our construction is based…

For certain symmetric isogeny $\lambda: A\rightarrow A^\vee$ of abelian varieties over a global field $F$, B. Poonen and E. Rains put an orthogonal quadratic structure on $\mathrm{H}^1(\mathbb{A}_F,A[\lambda])$ and realize the Selmer group…

We study smooth curves on abelian surfaces, especially for genus 4, when the complementary subvariety in the Jacobian is also a surface. We show that up to translation there is exactly one genus 4 hyperelliptic curve on a general (1,…

We introduce generalised orbit algebras. The purpose here is to measure how some combinatorial properties can characterize the action of a group of permutations on the subsets. The similarity with orbit algebras is such that it took the…

Jacobi brackets (a generalization of standard Poisson brackets in which Leibniz's rule is replaced by a weaker condition) are extended to brackets involving an arbitrary (even) number of functions. This new structure includes, as a…

We present simple graph-theoretic characterizations of Cayley graphs for monoids, semigroups and groups. We extend these characterizations to commutative monoids, semilattices, and abelian groups.

We study the transcendence of periods of abelian differentials, both at the arithmetic and functional level, from the point of view of the natural bi-algebraic structure on strata of abelian differentials. We characterise geometrically the…

In this article, we show that in each of four standard families of hyperelliptic curves, there is a density-$1$ subset of members with the property that their Jacobians have adelic Galois representation with image as large as possible. This…

The main purpose of this paper is to provide a second cohomology group of a (metric) Hom-Jacobi algebra with coefficients in a given representation. Moreover, we show that second cohomology group classifies abelian extensions of a (metric)…

We survey the theory of the compactified Jacobian associated to a singular curve. We focus on describing low genus examples using the Abel map.

Sidon spaces have been introduced by Bachoc, Serra and Z\'emor in 2017 as the $q$-analogue of Sidon sets. The interest on Sidon spaces has increased quickly, especially after the work of Roth, Raviv and Tamo in 2018, in which they…

We introduce linear Dirac and generalized complex structures on Cartan geometries and give criteria for Dirac subalgebras of $\frkg\ltimes\frkg^*$ representing Dirac structures on a Cartan geometry. We prove that there is a bijection…

We construct examples of complex algebraic surfaces not admitting normal embeddings (in the sense of semialgebraic or subanalytic sets) with image a complex algebraic surface.

We describe a generalization of the large sieve to situations where the underlying groups are nonabelian, and give several applications to the arithmetic of abelian varieties. In our applications, we sieve the set of primes via the system…