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Corpus ID: 235694371

New examples of Weierstrass semigroups associated with a double covering of a curve on a Hirzebruch surface of degree one

@inproceedings{Watanabe2021NewEO,
title={New examples of Weierstrass semigroups associated with a double covering of a curve on a Hirzebruch surface of degree one},
author={Kenta Watanabe},
year={2021}
}

Let φ : Σ1 −→ P 2 be a blow up at a point on P2. Let C be the proper transform of a smooth plane curve of degree d ≥ 4 by φ, and let P be a point on C. Let π : C̃ −→ C be a double covering branched along the reduced divisor on C obtained as the intersection of C and a reduced divisor in | − 2KΣ1 | containing P . In this paper, we investigate the Weierstrass semigroup H(P̃ ) at the ramification point P̃ of π over P , in the case where the intersection multiplicity at φ(P ) of φ(C) and the… Expand

Let X be a K3 surface with Picard number one which is given by a double cover π:X→ℙ2. Let C be a smooth curve on X with π−1π(C)=C which is not the ramification divisor of π, and let P be a… Expand

Let C be a complete non-singular curve of genus 3 over an algebraically closed field of characteristic 0. We determine all possible Wierstrass semigroups of ramification points on double coverings of… Expand

Let $$\Sigma _1$$Σ1 be a Hirzebruch surface of degree one. Let C be a smooth curve on $$\Sigma _1$$Σ1 which is given as the proper transform of a smooth plane curve $$C_0$$C0 of degree $$d\ge 4$$d≥4… Expand

We classify all semigroups each of which arises as a Weierstrass semigroup at a pair of inflection points of multiplicities d or d-1 on a smooth plane curve of degree d.

Let $$C$$C be a smooth plane curve of degree $$d, P$$d,P be a point on $$C$$C, and let $$\pi :\tilde{C}\rightarrow C$$π:C~→C be a double covering of the curve $$C$$C with the branch point $$P$$P. In… Expand