Euler characteristic of primitive T-hypersurfaces and maximal surfaces

Details Euler characteristic of primitive T-hypersurfaces and maximal surfaces Euler characteristic of primitive T-hypersurfaces and maximal surfaces

2006-02-23

arxiv.org/abs/math/0602534v2

Mathematics

Algebraic Geometry

26 pages, 11 figures, one reference added, notation changed

Scientific paper

Viro method plays an important role in the study of topology of real algebraic hypersurfaces. The T-primitive hypersurfaces we study here appear as the result of Viro's combinatorial patchworking when one starts with a primitive triangulation. We show that the Euler characteristic of the real part of such a hypersurface of even dimension is equal to the signature of its complex part. We use this result to prove the existence of maximal surfaces in some three-dimensional toric varieties, namely those corresponding Nakajima polytopes. In fact, these results belong to the field of tropical geometry and we explain how they can be understood tropically.

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