Related papers: Period Constraints on Hyperelliptic Branch Points

In this note, I study a comparison map between a motivic and \'{e}tale cohomology group of an elliptic curve over $\mathbb{Q}$ just outside the range of Voevodsky's isomorphism theorem. I show that the property of an appropriate version of…

We give effective upper bounds for the number of purely inseparable points on non isotrivial curves over function fields of positive characteristic and of transcendence degree one. These bounds depend on the genus of the curve, the genus of…

In this paper we consider graphs whose edges are associated with a degree of {\em importance}, which may depend on the type of connections they represent or on how recently they appeared in the scene, in a streaming setting. The goal is to…

In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…

Tessellations of the hyperbolic spaces by regular polygons are becoming popular because they support discrete quantum and classical models displaying unique spectral and topological characteristics. Resolving the true bulk spectra and the…

The moduli space for polarized hyperk\"ahler manifolds of $\mathrm{K3}^{[m]}$-type or $\mathrm{Kum}_m$-type with a given polarization type is not necessarily connected, which is a phenomenon that only happens for $m$ large. The period map…

We produce a flexible tool for contracting subcurves of logarithmic hyperelliptic curves, which is local around the subcurve and commutes with arbitrary base-change. As an application, we prove that hyperelliptic multiscale differentials…

We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has non-vanishing symplectic homology. As a consequence, we establish the existence of contractible closed…

We propose a holographic formalism for a timelike entanglement entropy in non-conformal theories. This pseudoentropy is a complex-valued measure of information, which, in holographic non-conformal theories, receives contributions from a set…

Globally hyperbolic spacetimes admitting infinitely many causal (and timelike) homotopy classes of curves joining two prescribed points, are exhibited and discussed.

We establish asymptotic lower bounds for the number of elliptic curves over $\mathbb{Q}$ with prescribed entanglement of division fields, ordered by naive height. Such elliptic curves are obtained as $1$-parameter families arising from…

We prove that the period mapping is dominant for elliptic surfaces over an elliptic curve with 12 nodal fibers, and that its degree is larger than 1.

Within the synthetic-geometric framework of Lorentzian (pre-)length spaces developed in Kunzinger and S\"amann (Ann. Glob. Anal. Geom. 54(3):399--447, 2018) we introduce a notion of a hyperbolic angle, an angle between timelike curves and…

Sufficient conditions are given for the computation of accessing arcs and arcs that links boundary components of multiply connected domains. The existence of a not-computably-accessible but computable point on a computably compact arc is…

We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the…

The periodic points of a morphism of good reduction for a smooth projective curve with good reduction over the p-adics form a discrete set. This is used to give an interpretation of the morphic height in terms of asymptotic properties of…

In Euclidean space there is a trivial upper bound on the maximum length of a compound "walk" built up of variable-length jumps, and a considerably less trivial lower bound on its minimum length. The existence of this non-trivial lower bound…

This paper examines the relationship between the automorphism group of a hyperelliptic curve defined over an algebraically closed field of characteristic two and the 2-rank of the curve. In particular, we exploit the wild ramification to…

We begin by introducing the concept of a Hodge structure and give some of its basic properties, including the Hodge and Lefschetz decompositions. We then define the period map, which relates families of Kahler manifolds to the families of…

Recently, a new set of multigraph parameters was defined, called "gonalities". Gonality bears some similarity to treewidth, and is a relevant graph parameter for problems in number theory and multigraph algorithms. Multigraphs of gonality 1…