Inflection Points of Real and Tropical Plane Curves

Erwan Brugallé and Lucia López de Medrano

Journal of Singularities
volume 4 (2012), 74-103

Received: 6 June 2011. Received in revised form: 15 February 2012.

DOI: 10.5427/jsing.2012.4e

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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.


Tropical geometry, Patchworking, Inflection points, Tropical modifications, Real algebraic curves

Author(s) information:

Erwan A. Brugallé L. López de Medrano
Université Pierre et Marie Curie, Paris 6, Unidad Cuernavaca del Instituto de Matemáticas
4 place Jussieu Universidad Nacional Autonoma de México
75005 Paris, France Cuernavaca, México
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