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arXiv · 1706.03733

Generalized Weierstrass semigroups and their Poincar\'e series

Julio José Moyano-Fernández·Wanderson Tenório·Fernando Torres
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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.

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Julio José Moyano-Fernández, Wanderson Tenório, Fernando Torres. 2017-06-12. Generalized Weierstrass semigroups and their Poincar\'e series. https://doi.org/10.1016/j.ffa.2019.03.005

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