English

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.

Keywords

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

R2 v1 2026-06-22T20:16:33.965Z