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math.AG2026

Projective symmetries of Chebyshev polynomials

Saeed Tafazolian, Jaap Top

Let $k$ be an algebraically closed field of odd characteristic $p$ , and let $φ_{d}$ be the monic Chebyshev polynomial defined by $φ_{d} (t + t^{- 1}) = t^{d} + t^{- d}$ . For $d > 4$ with $p ∤ d$ …

math.AG2025

Explicit Families of Hyperelliptic Curves with CM Jacobians

Saeed Tafazolian, Jaap Top

We construct explicit families of hyperelliptic curves over $\QQ$ whose Jacobians admit complex multiplication (CM). Each curve in these families is defined by \[ v^2 = (u+2)\,φ_d(…

math.AG2025

Locally recoverable codes with multiple recovering sets from maximal curves

Saeed Tafazolian, Jaa Top

In this paper, we present a construction of locally recoverable codes (LRCs) with multiple recovery sets using algebraic curves with many rational points. By leveraging separable m…

math.AG2024

Tate-Shafarevich results for quartic twists in characteristic $2$

Herivelto Borges, João Paulo Guardieiro, Cecília Salgado +1

The aim of this paper is to present elliptic curves defined over function fields of even characteristic having arbitrarily large Mordell-Weil rank. More precisely, we study ellipti…

Projective symmetries of Chebyshev polynomials

Explicit Families of Hyperelliptic Curves with CM Jacobians

Locally recoverable codes with multiple recovering sets from maximal curves

Tate-Shafarevich results for quartic twists in characteristic 2

Tate-Shafarevich results for quartic twists in characteristic $2$