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It is interesting to compare the Euler characteristic of the real part of a real
algebraic variety to the signature of its complex part. For example, a theorem by
Itenberg and Bertrand states that both quantities are equal for "primitive
T-hypersurfaces". After defining these latter, I will give a motivic proof of this
theorem via the motivic nearby fiber of a real semi-stable degeneration. This proof
extends in particular the original statement by Itenberg and Bertrand to non-singular
tropical varieties.
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