Geodesic
Inflection Points of Real and Tropical Plane Curves
Journal of Singularities, Tome 4 (2012), pp. 74-103

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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. 
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     author = {Erwan Brugall\'e and Lucia L\'opez de Medrano},
     title = {Inflection {Points} of {Real} and {Tropical} {Plane} {Curves}},
     journal = {Journal of Singularities},
     pages = {74--103},
     publisher = {mathdoc},
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     year = {2012},
     doi = {10.5427/jsing.2012.4e},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2012.4e/}
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Erwan Brugallé; Lucia López de Medrano. Inflection Points of Real and Tropical Plane Curves. Journal of Singularities, Tome 4 (2012), pp. 74-103. doi: 10.5427/jsing.2012.4e

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