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 (λ0, ..., λn). We see how the singularities of P (λ0, ..., λn) 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 λj/Σλi if we wish X to have only terminal (or canonical) singularities.
"Bounds on fake weighted projective space." Kodai Math. J. 32 (2) 197 - 208, June 2009. https://doi.org/10.2996/kmj/1245982903