Real inflection points of real hyperelliptic curves

Given a real hyperelliptic algebraic curve X with non-empty real part and a real effective divisor \mathcal {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 \vert\mathcal {D}\vert on X....

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2019-10, Vol.372 (7), p.4805-4827
Main Authors: Biswas, Indranil, Cotterill, Ethan, Garay López, Cristhian
Format: Article
Language:English
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Summary:Given a real hyperelliptic algebraic curve X with non-empty real part and a real effective divisor \mathcal {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 \vert\mathcal {D}\vert 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:0002-9947
1088-6850
DOI:10.1090/tran/7721