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Inflection points of real and tropical plane curves. (English) Zbl 1292.14042
Summary: 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.

MSC:
 14T05 Tropical geometry (MSC2010) 14P05 Real algebraic sets
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