Gilberto B. Almeida

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20212026

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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

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.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…

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

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

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

$a$ -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