  We study an obstruction to prescribing the dual complex of a strict
semistable degeneration of an algebraic surface. In particular, we show that if
$\Delta$ is a complex homeomorphic to a 2-dimensional manifold with negative
Euler characteristic, then $\Delta$ is not the dual complex of any semistable
degeneration. In fact, our theorem is somewhat more general and applies to some
complexes homotopy equivalent to such a manifold. Our obstruction is provided
by the theory of tropical complexes.
