Weierstrass semigroups on double covers of genus four curve
S. J. Kim, J. Komeda

TL;DR
This paper classifies all possible Weierstrass semigroups at ramification points on double covers of a genus 4 curve with genus greater than 11, and constructs examples realizing these semigroups.
Contribution
It provides a complete classification of Weierstrass semigroups for ramification points on certain double covers of genus 4 curves and constructs explicit examples.
Findings
All possible Weierstrass semigroups identified
Explicit constructions of double covers with these semigroups
Results apply to covers with genus > 11
Abstract
Let C be a complete non-singular irreducible curve of genus 4 over an algebraically closed field of characteristic 0. We determine all possible Weierstrass semigroups of ramification points on double covers of C which have genus greater than 11. Moreover, we construct double covers with ramification points whose Weierstrass semigroups are the possible ones.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Polynomial and algebraic computation
