Zariski multiples associated with quartic curves

2022/09/24 by Ichiro Shimada, Shimada, Ichiro · 1 citation
Mathematics · #14H50 #14J26 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2209.11938

openalex publication_date 2022/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate Zariski multiples of plane curves Z₁, …, Z_N such that each Z_i is a union of a smooth quartic curve, some of its bitangents, and some of its 4-tangent conics. We show that, for plane curves of this type, the deformation types are equal to the homeomorphism types, and that the number of deformation types grows as O(d⁶²) when the degree d of the plane curves tends to infinity.

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