Nazar Arakelian

activity

20142026

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13 papers · 1 filter

math.AG2026

Algebraic curves admitting automorphism groups of large prime square order

Nazar Arakelian, Diego Kian

Let $K$ denote an algebraically closed field of arbitrary characteristic. In this paper we provide bounds for the size of a prime $ℓ$ for which there are curves defined…

math.AG2026

Frobenius nonclassicality of generalized Fermat curves with respect to conics

Nazar Arakelian, Leandro A. M. Rodrigues

The effective application of the Stöhr-Voloch theory for the linear system of plane curves of a fixed degree to bound the number of rational points of a family of plane curves defi…

math.AG2025

Curves on Frobenius nonclassical loci of hypersurfaces

Nazar Arakelian, Pietro Speziali

Let $S \subset P^{n}$ be an absolutely irreducible projective hypersurface defined over a finite field $F_{q}$ , equipped with the $F_{q}$ -Frobenius m…

math.AG2022

Duality for certain multi-Frobenius nonclassical curves in higher dimensional spaces

Nazar Arakelian

We show how a type of multi-Frobenius nonclassicality of a curve defined over a finite field $F_{q}$ of characteristic $p$ reflects on the geometry of its strict dual curve.…

math.AG2020

Algebraic curves with automorphism groups of large prime order

Nazar Arakelian, Pietro Speziali

Let $X$ be an algebraic curve of genus $g$ defined over an algebraically closed field $K$ of characteristic $p \geq 0$ , and $q$ a prime dividing $|\mbox{Aut}(\mathcal{X})…

math.AG2019

Separable degree of the Gauss map and strict dual curves over finite fields

Nazar Arakelian

Let $X$ be a projective algebraic curve and denote by $X^{^{'}}$ its strict dual curve. The map $γ : X ⟶ X^{^{'}}$ is called (strict)…

math.AG2018

The Hurwitz curve over a finite field and its Weierstrass points for the morphism of lines

Nazar Arakelian, Herivelto Borges, Pietro Speziali

For any smooth Hurwitz curve $H_{n} : X Y^{n} + Y Z^{n} + X^{n} Z = 0$ over the finite field $F_{p}$ , an explict description of its Weierstrass points for the morphism of lines…

math.AG2016

On the spectrum for the genera of maximal curves over small fields

Nazar Arakelian, Saeed Tafazolian, Fernando Torres

Motivated by previous computations in Garcia, Stichtenoth and Xing (2000) paper ,we discuss the spectrum $M (q^{2})$ for the genera of maximal curves over finite fields of or…

math.AG2016

Bounds for the number of points on curves over finite fields

Nazar Arakelian, Herivelto Borges

Let $X$ be a projective irreducible nonsingular algebraic curve defined over a finite field $F_{q}$ . This paper presents a variation of the Störh-Voloch theory and…

math.AG2016

On generalizations of Fermat curves over finite fields and their automorphisms

Nazar Arakelian, Pietro Speziali

Let $X$ be an irreducible algebraic curve defined over a finite field $F_{q}$ of characteristic $p > 2$ . Assume that the $F_{q}$ -automorphism group of $\mathc…

math.AG2015

Frobenius nonclassicality of Fermat curves with respect to cubics

Nazar Arakelian, Herivelto Borges

For Fermat curves $F : a X^{n} + b Y^{n} = Z^{n}$ defined over $F_{q}$ , we establish necessary and sufficient conditions for $F$ to be $F_{q}$ -Frobenius nonclas…

math.AG2015

A characterization of the Artin-Mumford curve

Nazar Arakelian, Gábor Korchmáros

Let $M$ be the Artin-Mumford curve over the finite prime field $F_{p}$ with $p > 2$ . By a result of Valentini and Madan, $\mbox{Aut}_{\mathbb{F}_p}(\mathcal{M})\cong…

math.AG2014

Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree

Nazar Arakelian, Herivelto Borges

For each integer $s \geq 1$ , we present a family of curves that are $F_{q}$ -Frobenius nonclassical with respect to the linear system of plane curves of degree s. In the case…