Generalized Weierstrass semigroups and Riemann-Roch spaces for certain curves with separated variables

Abstract

In this work we study the generalized Weierstrass semigroup H(P m ) at an m-tuple P m = (P 1 , . . . , P m ) of rational points on certain curves admitting a plane model of the form fIn particular, we compute the generating set Γ(P m ) of H(P m ) and, as a consequence, we explicit a basis for Riemann-Roch spaces of divisors with support in {P 1 , . . . , P m } on these curves, generalizing results of Maharaj, Matthews, and Pirsic in [14].

Generalized Weierstrass semigroups at several points on certain maximal curves which cannot be covered by the Hermitian curve

“…For further references and recent applications of these structures see [3,26,29]. It is worth mentioning that the generalized Weierstrass semigroup H(Q) is a different set than the (classical) Weierstrass semigroup H(Q) of X at Q presented in the previous section.…”

On Weierstrass Gaps at Several Points

“…In [8], Duursma and Park introduced the concept of discrepancies. As shown in [17], it is possible to express notion of absolute maximal elements in generalized Weierstrass semigroups by using discrepancies, which has shown an important tool for explicit computations. In the rest of this section, we explore such similar connections with relative maximal elements.…”

“…. , P a+1 }; see [17] for details. In the next result, we will explicit the relative maximal elements of H(P m ) in the region C(P m ).…”

“…These structures were recently explored in [16], where there is established connections between the concepts of maximal elements in [7] and generating sets for H(Q) in the sense of [15]. Explicit computations relying on the approach of [16] and its outcomes are presented in [17] for certain special curves with separable variables, denoted by X f,g (see Sec. 4).…”

Isometry-Dual Flags of Many-Point AG Codes

“…The present work can be seen as a generalization of the work started in [3]. Here we consider flags of many-point algebraic geometry codes and deal with the generalized Weierstrass semigroups introduced in [2] and also investigated in [16,21]. For Q t = (Q 1 , .…”