Inflection Points of Real and Tropical Plane Curves

Details Inflection Points of Real and Tropical Plane Curves Inflection Points of Real and Tropical Plane Curves

2011-02-12

arxiv.org/abs/1102.2478v4

Mathematics

Algebraic Geometry

29 pages, 20 figures. To be published in "Journal of Singularities"

Scientific paper

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.

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