Phase tropical varieties those are degenerations of complete intersections are topological manifolds

In the first part of this talk we show that a smooth complex projective complete intersection variety of arbitrary codimension can be decomposed into pairs-of-pants, where a $k$-dimensional pair-of-pants is diffeomorphic to the complement of $k+2$ generic hyperplanes in $\mathbb{CP}^k$. This generalizes an earlier theorem of Mikhalkin. Moreover, we prove that a phase tropical variety which is a degeneration of a smooth complete intersection varieties is a topological manifold. This gives a positive answer to Viro's conjecture in the case of complete intersections.