Toric Variety - Morphisms of Toric Varieties

Morphisms of Toric Varieties

Suppose that Δ₁ and Δ₂ are fans in lattices N₁ and N₂. If f is a linear map from N₁ to N₂ such that the image of every cone of Δ₁ is contained in a cone of Δ₂, then f induces a morphism f_* between the corresponding toric varieties. This map f_* is proper if and only if the map f maps |Δ₁| onto |Δ₂|, where |Δ| is the underlying space of a fan Δ given by the union of its cones.