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.
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Abstract:
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(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 |
| email: brugalle@math.jussieu.fr | email: lucia@matcuer.unam.mx |
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