On gap sets in arbitrary Kummer extensions of $K(x)$
Algebraic Geometry
2025-06-25 v1
Abstract
Let be an algebraically closed field, and let be a Kummer extension of function fields of genus . We provide a compact and explicit description of the gap set at any totally ramified place of the extension . As a consequence, we deduce structural properties of the Weierstrass semigroup ; in particular, we determine a generating set for , 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 relative to .
Cite
@article{arxiv.2506.19169,
title = {On gap sets in arbitrary Kummer extensions of $K(x)$},
author = {Ethan Cotterill and Erik A. R. Mendoza and Pietro Speziali},
journal= {arXiv preprint arXiv:2506.19169},
year = {2025}
}