Abstract
Abstract
We give a motivic proof of the fact that for nonsingular real tropical complete intersections, the Euler characteristic of the real part is equal to the signature of the complex part. This was originally proved by Itenberg in the case of surfaces in
$\mathbb {C}P^{3}$
, and has been successively generalized by Bertrand and by Bihan and Bertrand. Our proof, different from previous approaches, is an application of the motivic nearby fiber of semistable degenerations. In particular, it extends the original result by Itenberg, Bertrand, and Bihan to real analytic families admitting a
$\mathbb {Q}$
-nonsingular tropical limit.
Funder
Agence Nationale de la Recherche
Publisher
Cambridge University Press (CUP)
Cited by
1 articles.
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1. Combinatorial patchworking: Back from tropical geometry;Transactions of the American Mathematical Society;2024-07-29