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, ..., λ_n). We see how the singularities of P (λ₀, ..., λ_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 λ_j/Σλ_i if we wish X to have only terminal (or canonical) singularities.