The matroid structure of vectors of the Mordell-Weil lattice and the topology of plane quartics and bitangent lines

2019/02/13 by Ryutaro Sato, Sato, Ryutaro, Shinzo Bannai +1
Mathematics · #05B35 #14E20 #14J27 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1902.04723

openalex publication_date 2019/02/13 · openalex created_date 2019/02/21 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce the terminology of matroids into the study of Zariski-pairs related to rational elliptic surfaces, aiming to simplify the presentation and arguments involved. As an application, we provide new examples of Zariski N-ples of relatively low degree. Namely we show that a Zariski 102-ple of degree 18 exists.

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