Related papers: On certain N--sheeted coverings and numerical semi…

Let $\Gamma$ be a plane curve of degree $d$ with $\delta$ ordinary nodes and no other singularities. If $P$ is a smooth point on $\Gamma$ then the Weierstrass gap sequence at $P$ is considered as that at the corresponding point on the…

We contruct a one-to-one correspondence between a subset of numerical semigroups with genus $g$ and $\gamma$ even gaps and the integer points of a rational polytope. In particular, we give an overview to apply this correspondence to try to…

The aim of this paper is to present a few versions of the Riemann-Hurwitz formula for a regular branched covering of graphs. By a graph, we mean a finite connected multigraph. The genus of a graph is defined as the rank of the first…

Nonlinear Doebner-Goldin [Phys. Rev. A 54, 3764 (1996)] gauge transformations (NGT) defined in terms of a wave function $\psi(x)$ do not form a group. To get a group property one has to consider transformations that act differently on…

A curve in the plane is $x$-monotone if every vertical line intersects it at most once. A family of curves are called pseudo-segments if every pair of them have at most one point in common. We construct $2^{\Omega(n^{4/3})}$ families, each…

The aim of this paper is to show that any finite undirected bipartite graph can be considered as a polynomial $p \in \mathbb{N}[x]$, and any directed finite bipartite graph can be considered as a polynomial $p\in\mathbb{N}[x,y]$, and vise…

In line with the recent development in topological graph theory, we are considering undirected graphs that are allowed to contain {\em multiple edges}, {\em loops}, and {\em semi-edges}. A graph is called {\em simple} if it contains no…

We determine all modular curves X(N) (with $N\geq 7$) which are hyperelliptic or bielliptic. We make available a proof that the automorphism group of X(N) coincides with the normalizer of $\Gamma(N)$ in $\operatorname{PSL}_2(\mathbb{R})$.

Let $N$ be a closed, connected, and oriented Riemannian manifold, which admits a quasiregular $\omega$-curve $\mathbb{R}^n \to N$ with infinite energy. We prove that, if the de Rham class of $\omega$ is non-zero and belongs to a so-called…

Let S be a Dedekind scheme with field of functions K. We show that if X_K is a smooth connected proper curve of positive genus over K, then it admits a N\'eron model over S, i.e., a smooth separated model of finite type satisfying the usual…

For a metric space $X$ with a compatible measure $\mu$, Genevois and Tessera defined the Scaling Group of $(X,\mu)$ as the subgroup $\Gamma$ of $\mathbb{R}_{>0}$ of positive real numbers $\gamma$ for which there are quasi-isometries of $X$…

Let $H$ be a normal subgroup of a group $G$. The normal subgroup based power graph $\Gamma_H(G)$ of $G$ is the simple undirected graph with vertex set $V(\Gamma_H(G))= (G\setminus H)\cup \{e\}$ and two distinct vertices $a$ and $b$ are…

Suppose $S$ is an affine, noetherian scheme, $X$ is a separated, noetherian $S$-scheme, $\mathcal{E}$ is a coherent ${\mathcal{O}}_{X}$-bimodule and $\mathcal{I} \subset T(\mathcal{E})$ is a graded ideal. We study the geometry of the…

We explicitly describe the set of gaps and the Weierstrass semigroup at a totally ramified place of degree one on a Kummer extension defined by the affine equation $y^m = f(x)$ over $K$, an algebraic extension of $\mathbb{F}_q$, where…

Suppose that $X$ be a nonempty set. Denote by $\mathcal{T}(X)$ the full transformation semigroup on $X$. For $\varnothing \neq Z\subseteq Y\subseteq X$, let $\mathcal{T}(X,Y,Z)=\{\alpha \in \mathcal{T}(X): Y\alpha \subseteq Z \}$. Then…

A simple undirected graph is said to be {\em semisymmetric} if it is regular and edge-transitive but not vertex-transitive. Every semisymmetric graph is a bipartite graph with two parts of equal size. It was proved in [{\em J. Combin.…

We consider numerical semigroups associated with normal weighted homogeneous surface singularities with rational homology sphere links. We say that a semigroup is representable if it can be realized in this way. In this article, we study…

In this article we define stable supercurves and super stable maps of genus zero via labeled trees. We prove that the moduli space of stable supercurves and super stable maps of fixed tree type are quotient superorbifolds. To this end, we…

In this work, we investigate generalized Weierstrass semigroups in arbitrary Kummer extensions of function field $\mathbb{F}_q(x)$. We analyze their structure and properties, with a particular emphasis on their maximal elements. Explicit…

The modular variety of non singular and complete hyperelliptic curves with level-two structure of genus 3 is a 5-dimensional quasi projective variety which admits several standard compactifications. The first one, X, comes from the…