Generalized Weierstrass semigroups and their Poincaré series
arXiv:1706.03733 · doi:10.1016/j.ffa.2019.03.005
Abstract
We investigate the structure of the generalized Weierstrass semigroups at several points on a curve defined over a finite field. We present a description of these semigroups that enables us to deduce properties concerned with the arithmetical structure of divisors supported on the specified points and their corresponding Riemann-Roch spaces. This characterization allows us to show that the Poincaré series associated with generalized Weierstrass semigroups carry essential information to describe entirely their respective semigroups.
20 pages