On generalized Weierstrass Semigroups in arbitrary Kummer extensions of $\mathbb{F}_q(x)$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909582164492288 |
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| author | Castellanos, Alonso S. Mendoza, Erik A. R. Tizziotti, Guilherme |
| author_facet | Castellanos, Alonso S. Mendoza, Erik A. R. Tizziotti, Guilherme |
| contents | In this work, we investigate generalized Weierstrass semigroups in arbitrary Kummer extensions of function field $\mathbb{F}_q(x)$. We analyze their structure and properties, with a particular emphasis on their maximal elements. Explicit descriptions of the sets of absolute and relative maximal elements within these semigroups are provided. Additionally, we apply our results to function fields of the maximal curves $\mathcal{X}_{a,b,n,s}$ and $\mathcal{Y}_{n,s}$, which cannot be covered by the Hermitian curve, and the Beelen-Montanucci curve. Our results generalize and unify several earlier contributions in the theory of Weierstrass semigroups, providing new perspectives on the relationship between these semigroups and function fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12453 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On generalized Weierstrass Semigroups in arbitrary Kummer extensions of $\mathbb{F}_q(x)$ Castellanos, Alonso S. Mendoza, Erik A. R. Tizziotti, Guilherme Algebraic Geometry 14H55, 11G20 In this work, we investigate generalized Weierstrass semigroups in arbitrary Kummer extensions of function field $\mathbb{F}_q(x)$. We analyze their structure and properties, with a particular emphasis on their maximal elements. Explicit descriptions of the sets of absolute and relative maximal elements within these semigroups are provided. Additionally, we apply our results to function fields of the maximal curves $\mathcal{X}_{a,b,n,s}$ and $\mathcal{Y}_{n,s}$, which cannot be covered by the Hermitian curve, and the Beelen-Montanucci curve. Our results generalize and unify several earlier contributions in the theory of Weierstrass semigroups, providing new perspectives on the relationship between these semigroups and function fields. |
| title | On generalized Weierstrass Semigroups in arbitrary Kummer extensions of $\mathbb{F}_q(x)$ |
| topic | Algebraic Geometry 14H55, 11G20 |
| url | https://arxiv.org/abs/2504.12453 |