The geometry of three sections on certain rational elliptic surfaces and Mumford representations

2021/10/13 by Ryosuke Masuya, Masuya, Ryosuke
Computer Science · Mathematics · #14H50 #14J27 #14Q05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2110.06429

openalex publication_date 2021/10/13 · openalex created_date 2021/10/25 · openalex updated_date 2026/07/28

Abstract

In this article, we study the geometry of plane curves obtained by three sections and another section given as their sum on certain rational elliptic surfaces. We make use of Mumford representations of semi-reduced divisors in order to study the geometry of sections. As a result, we are able to give new proofs for some classical results on singular plane quartics and their bitangent lines.

Citations

• Representations of divisors on hyperelliptic curves, Gröbner bases and plane curves with quasi-toric relations

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