Real inflection points of real hyperelliptic curves

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 \(X\)....

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Bibliographic Details
Published inarXiv.org
Main Authors Biswas, Indranil, Cotterill, Ethan, Cristhian Garay López
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.10.2018
Subjects
Curves
Inflection points
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Summary: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.
ISSN:2331-8422