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Algebra i Analiz, 2018, Volume 30, Issue 1, Pages 20–31 (Mi aa1570)  

Research Papers

Nonexistence of torically maximal hypersurfaces

E. Brugalléa, G. Mikhalkinb, J.-J. Rislerc, K. Shawd

a École Polytechnique, Centre de Mathématiques, Laurent Schwartz, 91 128 Palaiseau Cedex, France
b Section de mathématiques, Université de Genève, Villa Battelle, 1227 Carouge, Suisse
c Université Pierre et Marie Curie, 4 Place Jussieu, 75 005 Paris, France
d Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany

Abstract: Torically maximal curves (known also as simple Harnack curves) are real algebraic curves in the projective plane such that their logarithmic Gauss map is totally real. In this paper it is shown that the hyperplanes in projective spaces are the only torically maximal hypersurfaces of higher dimensions.

Keywords: simple harnack curves, real algebraic toric hypersurfaces.

Funding Agency Grant Number
European Research Council TROPGEO
Swiss National Science Foundation 141329
159240
Alexander von Humboldt Postdoctoral Fellowship
Part of this work was done during the research stay of E. B. and J.-J. R. at the Centre Interfacultaire Bernoulli (Lausanne) in the framework of the program “Tropical geometry in its complex and symplectic aspects”. The authors are grateful to CIB for the support and excellent working conditions. Research of G. M. was supported in part by the grant TROPGEO of the European Research Council, by the grants 141329 and 159240 of the Swiss National Science Foundation, and by the NCCR SwissMAP of the Swiss National Science Foundation. Research of K. S. was supported by an Alexander von Humboldt Postdoctoral Fellowship.


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Document Type: Article
Received: 30.01.2017
Language: English

Citation: E. Brugallé, G. Mikhalkin, J.-J. Risler, K. Shaw, “Nonexistence of torically maximal hypersurfaces”, Algebra i Analiz, 30:1 (2018), 20–31

Citation in format AMSBIB
\Bibitem{BruMikRis18}
\by E.~Brugall\'e, G.~Mikhalkin, J.-J.~Risler, K.~Shaw
\paper Nonexistence of torically maximal hypersurfaces
\jour Algebra i Analiz
\yr 2018
\vol 30
\issue 1
\pages 20--31
\mathnet{http://mi.mathnet.ru/aa1570}
\elib{http://elibrary.ru/item.asp?id=32234329}


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