Every H-regular d-dimensional tropical subvariety of a tropical abelian variety has (−1)^d χ(X) ≥ 0, with counterexamples when H-regularity is dropped.
On the signed Euler characteristic property for subvarieties of abelian varieties
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Topology and Euler characteristics of tropical varieties
Every H-regular d-dimensional tropical subvariety of a tropical abelian variety has (−1)^d χ(X) ≥ 0, with counterexamples when H-regularity is dropped.