  Local models are certain schemes, defined in terms of linear-algebraic moduli
problems, which give \'etale-local neighborhoods of integral models of certain
p-adic PEL Shimura varieties defined by Rapoport and Zink. When the group
defining the Shimura variety ramifies at p, the local models (and hence the
Shimura models) as originally defined can fail to be flat, and it becomes
desirable to modify their definition so as to obtain a flat scheme. In the case
of unitary similitude groups whose localizations at Q_p are ramified,
quasi-split GU_n, Pappas and Rapoport have added new conditions, the so-called
wedge and spin conditions, to the moduli problem defining the original local
models and conjectured that their new local models are flat. We prove a
preliminary form of their conjecture, namely that their new models are
topologically flat, in the case n is odd.
