Real inflection points of real hyperelliptic curves

• Published in: arXiv.org
• Main Authors: Biswas, Indranil, Cotterill, Ethan, Cristhian Garay López
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 04.10.2018
• Subjects: Curves; Inflection points

Given a real hyperelliptic algebraic curve \(X\) with non-empty real part and a real effective divisor \(\mc{D}\) arising via pullback from \(\mathbb{P}^1\) under the hyperelliptic structure map, we study the real inflection points of the associated complete real linear series \(|\mc{D}|\) on \(X\). To do so we use Viro's patchworking of real plane curves, recast in the context of some Berkovich spaces studied by M. Jonsson. Our method gives a simpler and more explicit alternative to limit linear series on metrized complexes of curves, as developed by O. Amini and M. Baker, for curves embedded in toric surfaces.