Related papers: On maximal curves and unramified coverings

Torically maximal curves (known also as simple Harnack curves) are real algebraic curves in the projective plane such that their logarithmic Gau{\ss} map is totally real. In this paper we show that hyperplanes in projective spaces are the…

Based on fundamental properties of light scattering by a particle we reveal the existence of the ultimate upper limit for the light absorption by any partial mode. First, we obtain this result for scattering of a plane wave by a symmetric…

We give a bound on embedding dimensions of geometric generic fibers in terms of the dimension of the base, for fibrations in positive characteristic. This generalizes the well-known fact that for fibrations over curves, the geometric…

We investigate extremal metrics at which various types of rigidity theorems involving scalar curvatures hold. The rigidity we discuss here is related to the rigidity theorems presented by Mario Listing in his previous preprint. More…

We find an upper bound for the asymptotic dimension of a hyperbolic metric space with a set of geodesics satisfying a certain boundedness condition studied by Bowditch. The primary example is a collection of tight geodesics on the curve…

We show that every smooth projective curve over a finite field k admits a finite tame morphism to the projective line over k. Furthermore, we construct a curve with no such map when k is an infinite perfect field of characteristic two. Our…

A longstanding avenue of research in orientable surface topology is to create and enumerate collections of curves in surfaces with certain intersection properties. We look for similar collections of curves in non-orientable surfaces. A…

An instance of the graph-constrained max-cut (GCMC) problem consists of (i) an undirected graph G and (ii) edge-weights on a complete undirected graph on the same vertex set. The objective is to find a subset of vertices satisfying some…

Let $M$ be a closed complex submanifold in ${\mathbb C}^N$ with the complete K\"ahler metric induced by the Euclidean metric. Several finiteness theorems on the $L^p$ Bergman space of holomorphic sections of a given Hermitian line bundle…

We give an explicit construction of a closed curve with constant torsion and everywhere positive curvature. We also discuss the restrictions on closed curves of constant torsion when they are constrained to lie on convex surfaces.

In this paper we consider a generalization of a well known result by Veronese about rational normal curves. More precisely, given a collection of linear spaces in $\PP^n$ we study the existence of rational normal curves intersecting each…

We study the rigid analytic geometry of cyclic coverings of the projective line. We determine the defining equation of a cyclic covering of degree $p$ of the projective line by a Mumford curve over a complete discrete valuation field of…

In [3], it is proved that the quotient of an abelian variety $A$ by a finite order automorphism $g$ is uniruled if and only if some power of $g$ satisfies a numerical condition $0<\age(g^k)<1$. In this paper, we show that $\age(g^k)=1$ is…

We extend our previous analysis of Riemannian four-manifolds M admitting rigid supersymmetry to N=1 theories that do not possess a U(1)_R symmetry. With one exception, we find that M must be a Hermitian manifold. However, the presence of…

We study genus one curves that arise as 2-, 3- and 4-coverings of elliptic curves. We describe efficient algorithms for testing local solubility and modify the classical formulae for the covering maps so that they work in all…

We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to…

Let M be a hyperbolic 3-manifold with nonempty totally geodesic boundary. We prove that there are upper and lower bounds on the diameter of the skinning map of M that depend only on the volume of the hyperbolic structure with totally…

We discuss two elementary constructions for covers with fixed ramification in positive characteristic. As an application, we compute the number of certain classes of covers between projective lines branched at 4 points and obtain…

It is hereby established that, in Euclidean spaces of finite dimension, bounded self-contracted curves have finite length. This extends the main result of Daniilidis, Ley, and Sabourau (J. Math. Pures Appl. 2010) concerning continuous…

We consider curves which go around Whitney umbrella. Then we consider the geodesic and the normal curvatures, ruled surfaces generated by the normal vector and normal developable surfaces with respect to the tangent and bi-tangent vectors…