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arXiv · 1709.00263

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

Wanderson Tenório·Guilherme Tizziotti
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Abstract

In this work we study the generalized Weierstrass semigroup $\widehat{H} (\mathbf{P}_m)$ at an $m$-tuple $\mathbf{P}_m = (P_{1}, \ldots , P_{m})$ of rational points on certain curves admitting a plane model of the form $f(y) = g(x)$ over $\mathbb{F}_{q}$, where ${f(T),g(T)\in \mathbb{F}_q[T]}$. In particular, we compute the generating set $\widehatΓ(\mathbf{P}_m)$ of $\widehat{H} (\mathbf{P}_m)$ and, as a consequence, we explicit a basis for Riemann-Roch spaces of divisors with support in $\{P_{1}, \ldots , P_{m}\}$ on these curves, generalizing results of Maharaj, Matthews, and Pirsic.

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Wanderson Tenório, Guilherme Tizziotti. 2017-09-01. Generalized Weierstrass semigroups and Riemann-Roch spaces for certain curves with separated variables. https://arxiv.org/abs/1709.00263

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