Related papers: A note on families of hyperelliptic curves

In these notes we focus a bit on the complex case for some families of matrices and equivalences between them.

In this article we prove the explicit Mordell Conjecture for large families of curves. In addition, we introduce a method, of easy application, to compute all rational points on curves of quite general shape and increasing genus. The method…

We survey some results on toric topology.

In the present paper, we introduce some new families of elliptic curves with positive rank arrising from Pythagorean triples.

We exploit the theory of $\infty$-stacks to provide some basic definitions and calculational tools regarding stratified homotopy theory of stratified topological stacks.

We establish a family of parametric isoperimetric-type inequalities with multiple geometric quantities for closed convex curves. These inequalities hold under certain parameter conditions. We also prove the equality conditions. Some new…

Congruence families, i.e., $\ell$-adic convergence for well-defined arithmetic subsequences, is a commonplace phenomenon for the coefficients of modular forms. Such families superficially resemble one another, but they often vary…

We consider the stack of stable curves of genus g with a given dual graph and we give an explicit desingularization of its closure in the moduli stack of stable curves. We study in particular the one-dimensional substack of curves with at…

We present experimental evidence to support the widely held belief that one half of all elliptic curves have infinitely many rational points. The method used to gather this evidence is a refinement of an algorithm due to the author which is…

This is an introduction to Grothendieck's descent theory, with some stress on the general machinery of fibered categories and stacks.

This paper develops a basic theory of H-groups. We introduce a special quotient of H-groups and extend some algebraic constructions of topological groups to the category of H-groups and H-maps. We use these constructions to prove some…

We classify the connected-homogeneous digraphs with more than one end. We further show that if their underlying undirected graph is not connected-homogeneous, they are highly-arc-transitive.

We show that the Union-Closed Conjecture holds for the union-closed family generated by the cyclic translates of any fixed set.

We produce a new family of polynomials f(x) over fields K of characteristic 2 which are exceptional, in the sense that f(x)-f(y) has no absolutely irreducible factors in K[x,y] besides the scalar multiples of x-y; when K is finite, this…

Elliptic curves have a well-known and explicit theory for the construction and application of endomorphisms, which can be applied to improve performance in scalar multiplication. Recent work has extended these techniques to hyperelliptic…

It is our aim in this note to give a counter example to an argument used in the proof of the main theorem of the paper: On iterations for families of asymptotically pseudocontractive mappings, Applied Mathematics Letters, 24 (2011), 33-38…

We use sheaf theory and the six operations to define and study the (equivariant) homology of stacks. The construction makes sense in the algebraic, complex-analytic, or even topological categories.

We show the existence of families of elliptic curves over Q whose generic rank is at least 2 for the torsion groups Z/8Z and Z/2Z x Z/6Z. Also in both cases we prove the existence of infinitely many elliptic curves, which are parameterized…

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

We use Morse theory to prove that the Lefschetz Hyperplane Theorem holds for compact smooth Deligne-Mumford stacks over the site of complex manifolds. For $Z \subset X$ a hyperplane section, $X$ can be obtained from $Z$ by a sequence of…