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

摘要

In this work we study the generalized Weierstrass semigroup (H) over cap (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 f (y) = g(x) over F-q, where f (T), g(T) is an element of F-q [T]. In particular, we compute the generating set (Gamma) over cap (P-m) of (H) over cap (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 [20]. (C) 2019 Elsevier Inc. All rights reserved.