On generalized Weierstrass semigroups in linearized function fields

Erik Mendoza

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arXiv · 2606.01369

On generalized Weierstrass semigroups in linearized function fields

Erik Mendoza

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Abstract

In this article, using the notion of discrepancies, we study the generalized Weierstrass semigroup $\widehat{H}(\mathbf{Q})$, where $\mathbf{Q}$ is an $n$-tuple of distinct totally ramified places of degree one in a linearized function field. As a consequence, we characterize and explicitly determine the sets of absolute maximal elements $\widehat{\Gamma}(\mathbf{Q})$ and relative maximal elements $\widehat{\Lambda}(\mathbf{Q})$, generalizing the existing results in the literature. Finally, we apply our results to some classes of algebraic curves.

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Erik Mendoza. 2026-05-31. On generalized Weierstrass semigroups in linearized function fields. https://arxiv.org/abs/2606.01369

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