INFLECTION POINTS OF REAL AND TROPICAL PLANE CURVES

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Abstract

We prove that Viro's patchworking produces real algebraic curves with the\nmaximal number of real inflection points. In particular this implies that\nmaximally inflected real algebraic $M$-curves realize many isotopy types. The\nstrategy we adopt in this paper is tropical: we study tropical limits of\ninflection points of classical plane algebraic curves. The main tropical tool\nwe use to understand these tropical inflection points are tropical\nmodifications.\n

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