Bounds on fake weighted projective space

Abstract

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.