6 papers
-numbers of covers in characteristic two: semigroups and Riemann-Roch spaces
Gilberto B. Almeida Filho, Saeed Tafazolian, Stéfani C. Vieira
We compute the -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…
-Numbers, higher Cartier ranks and maximality of van der Geer-van der Vlugt curves
Gilberto B. Almeida Filho, Saeed Tafazolian, Stéfani C. Vieira
Let be an odd prime and let be the van der Geer-van der Vlugt curve over an algebraically closed field of characteristic , where $R(x)=\sum_{i=0}^{h}a_ix…
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, , and the genus spectrum of maximal curves over $\F_{64}$ is determined. The p…
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 . The Skabelund curve, introduced by D.~Skabelund as a cyclic c…
Gapsets and the -generalized Fibonacci sequences
Gilberto B. Almeida Filho, Matheus Bernardini
In this paper, we bring the terminology of the Kunz coordinates of numerical semigroups to gapsets and we generalize this concept to -extensions. It allows us to identify gapset…
On Pure k-sparse gapsets
Gilberto B. Almeida Filho, Matheus Bernardini
In this paper, we study gapsets and we focus on obtaining information on how the maximum distance between to consecutive elements influences the behaviour of the set. In particular…