Saeed Tafazolian

activity

20112026

collaborators

23 papers

math.AG2026

$a$ -numbers of covers in characteristic two: semigroups and Riemann-Roch spaces

Gilberto B. Almeida Filho, Saeed Tafazolian, Stéfani C. Vieira

We compute the $a$ -numbers of the Garcia-Güneri-Stichtenoth curves, the Beelen-Montanucci curves, and the Skabelund covers of Suzuki curves in characteristic two. The proofs use th…

math.AG2026

$a$ -Numbers, higher Cartier ranks and maximality of van der Geer-van der Vlugt curves

Gilberto B. Almeida Filho, Saeed Tafazolian, Stéfani C. Vieira

Let $p$ be an odd prime and let $C_{R}$ be the van der Geer-van der Vlugt curve $y^{p} - y = x R (x)$ over an algebraically closed field of characteristic $p$ , where $R(x)=\sum_{i=0}^{h}a_ix…

math.AG2026

A Quadratic Bound for Automorphism Groups of Curves of Positive $p$ -Rank in Odd Characteristic

Saeed Tafazolian

Let $X$ be a nonsingular projective curve of genus $g \geq 2$ over an algebraically closed field of odd characteristic $p$ . Giulietti and Korchmáros established a quadratic genus boun…

math.AG2026

Sharp bounds and gap phenomena for large $p$ -subgroups of automorphism groups of curves

Saeed Tafazolian

Let $X$ be a curve of genus $g \geq 2$ over an algebraically closed field of odd characteristic $p$ , and let $G = Aut (X)$ . A theorem of Giulietti and Korchmaros shows that if $…

math.AG2026

Cyclic automorphisms beyond the canonical bound

Ahmad Kazemifard, Saeed Tafazolian

Let X be a smooth projective curve of genus g >= 2 over an algebraically closed field K, and suppose that Aut(X) contains a cyclic subgroup G of order N > 2g - 2. The cases N >= 2g…

math.AG2026

Nonexistence of maximal curves of genus five over $\F_{64}$

Gilberto B. Almeida Filho, Saeed Tafazolian, Stéfani C. Vieira

We show that there is no maximal curve of genus five over $\F_{64}$. As a consequence, $N_{64} (5) = 140$ , and the genus spectrum of maximal curves over $\F_{64}$ is determined. The p…

math.AG2026

On the generalized Ree curve

Ahmad Kazemifard, Saeed Tafazolian

Let p be an odd prime, let q_0 := p^s with s >= 1, and put q := p q_0^2. We study the smooth projective curve R_{p,s} with function field F_q(x,y,z), y^q - y = x^{q_0}(x^q - x), z^…

math.AG2026

A classification of zero $p$ -rank curves with large automorphism groups in odd characteristic

Saeed Tafazolian

Let $\cX$ be a curve of genus $g \geq 2$ and $p$ -rank zero over an algebraically closed field of odd characteristic $p$ , and let $G\le\Aut(\cX)$ satisfy $∣ G ∣ > 24 g (g - 1)$ . We prove that…

math.AG2026

A characterization of the Ree curve

Saeed Tafazolian

Let $q = 3 q_{0}^{2}$ , where $q_{0} = 3^{s}$ and $s \geq 3$ . We prove that a smooth, projective, geometrically irreducible curve over $\F_q$ with $q^{3} + 1$ rational points and genus \[ \frac32q_0(q-…

math.AG2026

Transitive automorphism groups of maximal curves

Saeed Tafazolian

Let $q$ be an odd prime power and let $X$ be a maximal curve of genus at least two over $\F_{q^2}$. We prove that the automorphism group of $X$ acts transitively on its rational po…

math.AG2026

Nakajima-extremal Artin--Schreier covers of ordinary elliptic curves in characteristic $2$

Saeed Tafazolian

Let $k$ be an algebraically closed field of characteristic $2$ and let $q = 2^{h}$ , $h \geq 3$ . We construct ordinary bielliptic curves $X$ of genus $q + 1$ for which \[ \Aut(X)\cong \Dih(C…

math.AG2026

On Skabelund's Ray Class Field Covers of the Suzuki and Ree Curves

Saeed Tafazolian

Let $\Sm_q$ and $\Rm_q$ denote the Suzuki and Ree curves. Motivated by the Giulietti--Korchmáros curve, Skabelund constructed cyclic covers $\tSm_q$ and $\tRm_q$ of these curves an…

math.AG2026

Explicit LCP of MDS Codes and LCD Codes on Hyperelliptic Curves via Mumford Representation

Adler Marques, Yuri da Silva, Saeed Tafazolian

We study algebraic geometry codes on hyperelliptic curves of genus $g \geq 2$ equipped with a rational Weierstrass point, with a focus on complementarity properties. Our first cont…

math.AG2026

Jacobian algebras and variation of hyperplane sections

Giovanna Ilardi, Abbas Nasrollah Nejad, Saeed Tafazolian

We study the variation in moduli of hyperplane sections of a hypersurface $V (f) \subseteq P^{n}$ with at most isolated singularities. Using the Milnor algebra $M (f)$ , we give…

math.AG2026

On the Maximality, Weierstrass Semigroups, and Automorphism Group of the Curve $Y^{q + 1} = X^{n} (X^{n} + 1)$

João Paulo Guardieiro, Yuri da Silva, Saeed Tafazolian

We study the algebraic curve over $F_{q^{2}}$ defined by $y^{q + 1} = x^{n} (x^{n} + 1)$ , where $n$ is a positive integer coprime to the characteristic. We first prove (when $q$ is o…

math.AG2026

Construction of Non-special Divisors on Kummer Covers With Arbritary Ramification For LCP Codes

Adler Marques, Yuri da Silva, Saeed Tafazolian

Linear Complementary Pairs (LCP) of algebraic geometry (AG) codes offer strong resistance against side-channel and fault-injection attacks, but their construction depends criticall…

math.AG2026

Veronese Avoiding Hypersurfaces

Giovanna Ilardi, Abbas Nasrollah Nejad, Saeed Tafazolian

We introduce Veronese-Avoiding hypersurfaces, inspired by the theory of associated forms of Alper--Isaev. In the smooth case, we reinterpret their criterion via Macaulay inverse sy…

math.AG2025

Maximal Subcovers of the Skabelund Curve: Uniqueness via Genus and Automorphism Groups

Gilberto B. Almeida Filho, Saeed Tafazolian, Stéfani C. Vieira

We establish a rigidity phenomenon for a family of intermediate covers of the Skabelund curve over $F_{q^{4}}$ . The Skabelund curve, introduced by D.~Skabelund as a cyclic c…

math.AC2022

Hankel edge ideals of trees and (semi-)Hamiltonian graphs

Dariush Kiani, Sara Saeedi Madani, Saeed Tafazolian

In this paper, we study the Hankel edge ideals of graphs. We determine the minimal prime ideals of the Hankel edge ideal of labeled Hamiltonian and semi-Hamiltonian graphs, and we…

math.AC2019

The $a$ -number of Certain Hyperelliptic Curves

Vahid Nourozi, Farhad Rahmati, Saeed Tafazolian

In this paper, we compute a formula for the $a$ -number of certain hyperelliptic curves given by the equation $y^{2} = x^{m} + 1$ for infinitely many values of $m$ . The same question is st…

math.AG2019

On certain maximal hyperelliptic curves related to Chebyshev polynomials

Saeed Tafazolian, Jaap Top

We study hyperelliptic curves arising from Chebyshev polynomials. The aim of this paper is to characterize the pairs $(q, d)$ such that the hyperelliptic curve $\cC$ over a finite f…

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.AG2011

Covered by Lines and Conic Connected Varieties

Simone Marchesi, Alex Massarenti, Saeed Tafazolian

We study some properties of an embedded variety covered by lines and give a numerical criterion ensuring the existence of a singular conic through two of its general points. We sho…

a-numbers of covers in characteristic two: semigroups and Riemann-Roch spaces

a-Numbers, higher Cartier ranks and maximality of van der Geer-van der Vlugt curves

A Quadratic Bound for Automorphism Groups of Curves of Positive p-Rank in Odd Characteristic

Sharp bounds and gap phenomena for large p-subgroups of automorphism groups of curves

Cyclic automorphisms beyond the canonical bound

Nonexistence of maximal curves of genus five over $\F_{64}$

On the generalized Ree curve

A classification of zero p-rank curves with large automorphism groups in odd characteristic

A characterization of the Ree curve

Transitive automorphism groups of maximal curves

Nakajima-extremal Artin--Schreier covers of ordinary elliptic curves in characteristic 2

On Skabelund's Ray Class Field Covers of the Suzuki and Ree Curves

Explicit LCP of MDS Codes and LCD Codes on Hyperelliptic Curves via Mumford Representation

Jacobian algebras and variation of hyperplane sections

On the Maximality, Weierstrass Semigroups, and Automorphism Group of the Curve Yq+1=Xn(Xn+1)

Construction of Non-special Divisors on Kummer Covers With Arbritary Ramification For LCP Codes

Veronese Avoiding Hypersurfaces

Maximal Subcovers of the Skabelund Curve: Uniqueness via Genus and Automorphism Groups

Hankel edge ideals of trees and (semi-)Hamiltonian graphs

The a-number of Certain Hyperelliptic Curves

On certain maximal hyperelliptic curves related to Chebyshev polynomials

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

Covered by Lines and Conic Connected Varieties

$a$ -numbers of covers in characteristic two: semigroups and Riemann-Roch spaces

$a$ -Numbers, higher Cartier ranks and maximality of van der Geer-van der Vlugt curves

A Quadratic Bound for Automorphism Groups of Curves of Positive $p$ -Rank in Odd Characteristic

Sharp bounds and gap phenomena for large $p$ -subgroups of automorphism groups of curves

A classification of zero $p$ -rank curves with large automorphism groups in odd characteristic

Nakajima-extremal Artin--Schreier covers of ordinary elliptic curves in characteristic $2$

On the Maximality, Weierstrass Semigroups, and Automorphism Group of the Curve $Y^{q + 1} = X^{n} (X^{n} + 1)$

The $a$ -number of Certain Hyperelliptic Curves