I have a fairly good understanding of what the dual of a projective space is. I am currently interested in weighted projective space but I haven't found anything on the construction of its dual space if it exists. At the same time I can't see how I can extend the definition of the usual dual projective space to the weighted one. Could anyone tell me if such a construction exists and if it does direct me to any usual reference of define it for me?

Thank you.

`$\textbf{GL}_V \cong \textbf{GL}_{V^\vee}$`

, where $V^\vee$ is the dual vector space. Thus every (injective) morphism of group schemes $\lambda:\mathbb{G}_m\to \textbf{GL}_V$ with "positive weights" induces also $\lambda^\vee:\mathbb{G}_m \to \textbf{GL}_{V^\vee}$. However, the natural bilinear pairing $V\times V^\vee \to \mathbb{A}^1$ is "bi-equivariant" for`$(\lambda,\lambda^vee)$`

if and only if $\lambda$ is the center. So do not expect a universal family of Cartier divisors. – Jason Starr Jan 18 '13 at 17:44