Generalized Weierstrass semigroups and their Poincar\'e series
Algebraic Geometry
2025-01-17 v1
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 Poincar\'e series associated with generalized Weierstrass semigroups carry essential information to describe entirely their respective semigroups.
Cite
@article{arxiv.1706.03733,
title = {Generalized Weierstrass semigroups and their Poincar\'e series},
author = {Julio José Moyano-Fernández and Wanderson Tenório and Fernando Torres},
journal= {arXiv preprint arXiv:1706.03733},
year = {2025}
}
Comments
20 pages