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

Excluded homeomorphism types for dual complexes of surfaces