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Euler characteristic of primitive T-hypersurfaces and maximal surfaces

Part of: Special varieties Polytopes and polyhedra

Published online by Cambridge University Press:  23 July 2009

Benoit Bertrand
Benoit Bertrand
Affiliation:
Institut de Mathématiques de Toulouse, IUT de Tarbes, 1 rue Lautréamont, BP 1624, 65016 Tarbes cedex, France (benoit.bertrand@iut-tarbes.fr)
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Abstract

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.

Keywords

Viro methodcombinatorial patchworkingtropical geometrytopology of real algebraic varietiestropical hypersurfacestoric varieties

MSC classification

Secondary: 14P25: Topology of real algebraic varieties 14M25: Toric varieties, Newton polyhedra 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry)
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 9 , Issue 1 , January 2010 , pp. 1 - 27
Copyright
Copyright © Cambridge University Press 2010

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