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tropical hypersurfaces

Journal of the Institute of Mathematics of Jussieu (1)

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1 results

Euler characteristic of primitive T-hypersurfaces and maximal surfaces
Part of
- Polytopes and polyhedra
- Special varieties
Benoit Bertrand
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 9 / Issue 1 / January 2010

Published online by Cambridge University Press:

23 July 2009, pp. 1-27

Print publication:

January 2010
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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 explain how this can be understood in tropical geometry. We use this result to prove the existence of maximal surfaces in some three-dimensional toric varieties, namely those corresponding to Nakajima polytopes.