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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.19169 |
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Table of Contents:
- Let $K$ be an algebraically closed field, and let $F/K(x)$ be a Kummer extension of function fields of genus $g$. We provide a compact and explicit description of the gap set $G(Q)$ at any totally ramified place $Q$ of the extension $F/K(x)$. As a consequence, we deduce structural properties of the Weierstrass semigroup $H(Q)$; in particular, we determine a generating set for $H(Q)$, and we characterize its symmetry in certain cases. We also generalize a formula due to Towse that describes the asymptotic behavior of the sum of the Weierstrass weights at all totally ramified places of the extension $F/K(x)$ relative to $g^3-g$.