Let $X$ be a complete toric variety over a field $k$. Its Picard scheme is defined to be the scheme representing the functor $Pic_{(X/k)(\text{fppf})}$, where $Pic_{X/k}: Sch_k^{op}\to Set$ sends a scheme $T$ over $k$ to the scheme $Pic(X\times T)/p_2^*Pic(T)$, and "(fppf)" denotes the sheafification of this functor w.r.t the fppf topology.

It is known that in this case the Picard scheme exists.

I want to know if there is any good combinatorial description of the Picard scheme. (We may assume $k=\mathbb{C}$ if this helps.)

normalcomplete toric, although I had the impression that normality is sometimes included in the definition of toric variety. – Donu Arapura Apr 22 '11 at 15:38