Weighted projective space

Properties

• If d is a positive integer then P is isomorphic to P, so one can without loss of generality assume that any set of n variables a have no common factor greater than 1. In this case the weighted projective space is called well-formed.
• The only singularities of weighted projective space are cyclic quotient singularities.
• A weighted projective space is a Q-Fano variety and a toric variety.
• The weighted projective space P is isomorphic to the quotient of projective space by the group that is the product of the groups of roots of unity of orders a₀,a₁,...,a_n acting diagonally.