Non-existence of torically maximal hypersurfaces

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 we show that hyperplanes in projective spaces are the only torically maximal hypersurfaces of higher dimensions.

10 pages. V2 merges the first version of this paper with the first version of arXiv:1510.00267