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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Real inflection points of real hyperelliptic curves


Authors: Indranil Biswas, Ethan Cotterill and Cristhian Garay López
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 14C20, 14T05, 14N10, 14P25
DOI: https://doi.org/10.1090/tran/7721
Published electronically: May 30, 2019
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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 $ \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.


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Additional Information

Indranil Biswas
Affiliation: School of Mathematics, Tata Institute for Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
Email: indranil@math.tifr.res.in

Ethan Cotterill
Affiliation: Instituto de Matemática, UFF, Rua Mário Santos Braga, S/N, 24020-140 Niterói RJ, Brazil
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

DOI: https://doi.org/10.1090/tran/7721
Keywords: Real enumerative algebraic geometry, tropical geometry, real linear series, real inflection points, real algebraic curves.
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.
Article copyright: © Copyright 2019 American Mathematical Society