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
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.
simple harnack curves, real algebraic toric hypersurfaces.
|European Research Council
|Swiss National Science Foundation
|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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E. Brugallé, G. Mikhalkin, J.-J. Risler, K. Shaw, “Nonexistence of torically maximal hypersurfaces”, Algebra i Analiz, 30:1 (2018), 20–31
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\by E.~Brugall\'e, G.~Mikhalkin, J.-J.~Risler, K.~Shaw
\paper Nonexistence of torically maximal hypersurfaces
\jour Algebra i Analiz
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