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Weierstrass semigroups for maximal curves realizable as Harbater–Katz–Gabber covers
- Source :
- Advances in Geometry. 22:445-450
- Publication Year :
- 2022
- Publisher :
- Walter de Gruyter GmbH, 2022.
-
Abstract
- We present a necessary and sufficient condition for a maximal curve, defined over the algebraic closure of a finite field, to be realised as an HKG-cover. We use an approach via pole numbers in a rational point of the curve. For this class of curves, we compute their Weierstrass semigroup as well as the jumps of their higher ramification filtrations at this point, the unique ramification point of the cover.
- Subjects :
- Geometry and Topology
Subjects
Details
- ISSN :
- 16157168 and 1615715X
- Volume :
- 22
- Database :
- OpenAIRE
- Journal :
- Advances in Geometry
- Accession number :
- edsair.doi...........c19133cbce551500cbfacd511a5bca79