Inflection Points of Real and Tropical Plane Curves

By Erwan Brugallé, Luc'ia L'opez de Medrano. 2011

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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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/45dc76d530398c063d46602a8728b2d1f21ba970