A faithful action of Gal($\overline{\mathbb{Q}}/\mathbb{Q}$) on Zariski multiplets

Abstract

In this work, we establish two main results in the context of arithmetic and geometric properties of plane curves. First, we construct numerous new examples of arithmetic Zariski pairs and multiplets, where only a few ones were previously available. Second, we describe a faithful action of the absolute Galois group on the equisingular strata of plane curves, providing insights into the interplay between Galois representations and the geometry of singular plane curves. We conclude the paper with very concretes examples of the general results obtained.