Related papers: Generalized Weierstrass semigroups and Riemann-Roc…

Let C be a complete non-singular irreducible curve of genus 4 over an algebraically closed field of characteristic 0. We determine all possible Weierstrass semigroups of ramification points on double covers of C which have genus greater…

Let C be the union of two general connected, smooth, nonrational curves X and Y intersecting transversally at a point P. Assume that P is a general point of X or of Y. Our main result, in a simplified way, says: Let Q be a point of X. Then…

In this work, subcovers $\mathcal{X}_{n,r}^s$ of the curve $\mathcal{X}_{n,r}$ are constructed, the Weierstrass semigroup $H(P_\infty)$ at the point $P_\infty \in \mathcal{X}_{n,r}^s$ is determined and the corresponding one-point AG codes…

Let $(S,H)$ be a generalized Fermat pair of the type $(k,n)$. If $F\subset S$ is the set of fixed points of the non-trivial elements of the group $H$, then $F$ is exactly the set of hyperosculating points of the standard embedding…

The Weierstrass curve is a pointed curve $(X,\infty)$ with a numerical semigroup $H_X$, which is a normalization of the curve given by the Weierstrass canonical form, $y^r + A_{1}(x) y^{r-1} + A_{2}(x) y^{r-2} +\dots + A_{r-1}(x) y +…

In 2017, D. Skabelund constructed a maximal curve over $\mathbb{F}_{q^4}$ as a cyclic cover of the Suzuki curve. In this paper we explicitly determine the structure of the Weierstrass semigroup at any point $P$ of the Skabelund curve. We…

Let $M$ be a subset of vector space or projective space. The authors define the \emph{generalized configuration space} of $M$ which is formed by $n$-tuples of elements of $M$ where any $k$ elements of each $n$-tuple are linearly…

We present an algorithm to compute bases for the spaces L(G), provided G is a rational divisor over a non-singular absolutely irreducible algebraic curve, and also another algorithm to compute the Weierstrass semigroup at P together with…

For an (imaginary) hyperelliptic curve $ \mathcal{H} $ of genus $g$, with a Weierstrass point $\Omega$, taken as the point at infinity, we determine a basis of the Riemann-Roch space $\mathcal{L}(\Delta + m \Omega)$, where $\Delta$ is of…

Let $\varphi:\Sigma_1\longrightarrow \mathbb{P}^2$ be a blow up at a point on $\mathbb{P}^2$. Let $C$ be the proper transform of a smooth plane curve of degree $d\geq 4$ by $\varphi$, and let $P$ be a point on $C$. Let…

Given a hyperelliptic curve $C$ of genus $g$ over a number field $K$ and a Weierstrass model $\mathscr{C}$ of $C$ over the ring of integers ${\mathcal O}_K$ (i.e. the hyperelliptic involution of $C$ extends to $\mathscr{C}$ and the quotient…

In this article we explicitly determine the Weierstrass semigroup at any place of some $\mathbb{F}_{q^2}$-maximal Fermat function fields $\mathcal{F}_m$, namely for $m=(q+1)/2$ and $m=(q+1)/3$. These famous function fields arise as Galois…

We continue the investigation of curves of type p,q started in [KKW]. We study the space of such curves and the space of nodal curves with prescribed Weierstra\ss semigroup. A necessary and sufficient criterion for a numerical semigroup to…

The relation of the Weierstrass semigroup with several invariants of a curve is studied. For Galois covers of curves with group $G$ we introduce a new filtration of the group decomposition subgroup of $G$. The relation to the ramification…

In this article we explicitly determine the Weierstrass semigroup at any point and the full automorphism group of a known $\mathbb{F}_{q^2}$-maximal curve $\mathcal{X}_3$ having the third largest genus. This curve arises as a Galois…

We extend results on Weierstrass semigroups at ramified points of double covering of curves to any numerical semigroup whose genus is large enough. As an application we strengthen the properties concerning Weierstrass weights in \cited{To}.

We show that three numerical semigroups <5,6,7,8>, <3,7,8 > and <3,5> are of double covering type, i.e., the Weierstrass semigroups of ramification points on double covers of curves. Combining this with the results of Oliveira-Pimentel and…

Let $\mathcal{I}_{d,g,R}$ be the union of irreducible components of the Hilbert scheme whose general points parametrize smooth, irreducible, curves of degree $d$, genus $g$, which are non--degenerate in the projective space $\mathbb{P}^R$.…

Let $k,n \geq 2$ be integers. A generalized Fermat curve of type $(k,n)$ is a compact Riemann surface $S$ that admits a subgroup of conformal automorphisms $H \leq \mbox{Aut}(S)$ isomorphic to $\mathbb{Z}_k^n$, such that the quotient…

We determine the Weierstrass semigroup at one and two totally ramified places in a Kummer extension defined by the affine equation $y^{m}=\prod_{i=1}^{r} (x-\alpha_i)^{\lambda_i}$ over $K$, the algebraic closure of $\mathbb{F}_q$, where…