2011/02/12 by Erwan Brugallé, Brugallé, Erwan, Lucía López de Medrano +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Polynomial and algebraic computation #math.AG
paper · pdf · doi:10.48550/arxiv.1102.2478
29 pages, 20 figures. To be published in "Journal of Singularities"
openalex publication_date 2011/02/12 · arxiv created 2012/03/06 · arxiv updated 2012/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that Viro's patchworking produces real algebraic curves with the maximal number of real inflection points. In particular this implies that maximally inflected real algebraic M-curves realize many isotopy types. The strategy we adopt in this paper is tropical: we study tropical limits of inflection points of classical plane algebraic curves. The main tropical tool we use to understand these tropical inflection points are tropical modifications.