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

2017/09/01 by Tenório, Wanderson, Tizziotti, Guilherme
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1709.00263

Abstract

In this work we study the generalized Weierstrass semigroup \widehatH (P_m) at an m-tuple P_m = (P₁, … , P_m) of rational points on certain curves admitting a plane model of the form f(y) = g(x) over \mathbbF_q, where f(T),g(T)∈ \mathbbF_q[T]. In particular, we compute the generating set \widehatΓ(P_m) of \widehatH (P_m) and, as a consequence, we explicit a basis for Riemann-Roch spaces of divisors with support in \P₁, … , P_m\ on these curves, generalizing results of Maharaj, Matthews, and Pirsic.

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