  A fake weighted projective space X is a Q-factorial toric variety with Picard
number one. As with weighted projective space, X comes equipped with a set of
weights (\lambda_0,...,\lambda_n). We see how the singularities of
P(\lambda_0,...,\lambda_n) influence the singularities of X, and how the
weights bound the number of possible fake weighted projective spaces for a
fixed dimension. Finally, we present an upper bound on the ratios
\lambda_j/\sum\lambda_i if we wish X to have only terminal (or canonical)
singularities.
