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

2021/07/01 by K. Watanabe, Watanabe, Kenta
Engineering · Mathematics · #14H55 #14J26 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2107.00202

openalex publication_date 2021/07/01 · openalex created_date 2022/08/27 · openalex updated_date 2026/07/28

Abstract

Let φ:Σ₁\longrightarrow ℙ² 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:C\longrightarrow C be a double covering branched along the reduced divisor on C obtained as the intersection of C and a reduced divisor in |-2K_Σ1| containing P. In this paper, we investigate the Weierstrass semigroup H(P) at the ramification point P of π over P, in the case where the intersection multiplicity at φ(P) of φ(C) and the tangent line at φ(P) of φ(C) is d-1.

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