Real inflection points of real hyperelliptic curves
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- by Indranil Biswas, Ethan Cotterill and Cristhian Garay López PDF
- Trans. Amer. Math. Soc. 372 (2019), 4805-4827 Request permission
Abstract:
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 $|\mathcal {D}|$ 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.
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Additional Information
- Indranil Biswas
- Affiliation: School of Mathematics, Tata Institute for Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
- MR Author ID: 340073
- Email: indranil@math.tifr.res.in
- Ethan Cotterill
- Affiliation: Instituto de Matemática, UFF, Rua Mário Santos Braga, S/N, 24020-140 Niterói RJ, Brazil
- MR Author ID: 763540
- Email: cotterill.ethan@gmail.com
- Cristhian Garay López
- Affiliation: Instituto de Matemática, UFF, Rua Mário Santos Braga, S/N, 24020-140 Niterói RJ, Brazil
- Email: cgaray@impa.br
- Received by editor(s): September 28, 2017
- Received by editor(s) in revised form: October 2, 2018
- Published electronically: May 30, 2019
- Additional Notes: The first author was supported by a J. C. Bose Fellowship.
The second author was supported by CNPq grant 309211/2015-8.
The third author was supported by a CNPq PDJ fellowship, grant No. 401565/2014-9. - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 4805-4827
- MSC (2010): Primary 14C20, 14T05, 14N10, 14P25
- DOI: https://doi.org/10.1090/tran/7721
- MathSciNet review: 4009441