The purpose of the present paper is threefold. First: giving a treatise on weighted projective spaces by the toric point of view. Second: providing characterizations of fans and polytopes giving weighted projective spaces, with particular focus on a kind of \emph{ recognition process} of toric data like fans and polytopes. Third: building a mathematical framework for the algorithmic and computational approach to wps's realized in [23,24].
Categories: math.AG