For questions related to toric geometry. The objects of study in toric geometry are toric varieties. Toric varieties are called ‘toric’ because they are equipped with a ‘torus action’. By a torus we mean the linear algebraic group $C^∗ ×\dots× C^∗$, not the torus from topology. A toric variety contains a torus as an open subset and this defines the torus action.

Toric geometry lies in the overlap of algebraic geometry (affine varieties) and polyhedral geometry (cones). In toric geometry we relate the gluing of varieties with the composition of cones.

The objects of study in toric geometry are toric varieties. These are geometric objects defined by combinatorial information. When we have a fan consisting of cones, we can define the toric variety of a fan by gluing together the affine toric varieties of the cones in the fan.

Toric varieties are called ‘toric’ because they are equipped with a ‘torus action’. By a torus we mean the linear algebraic group $C^∗ ×\dots× C^∗$, not the torus from topology. A toric variety contains a torus as an open subset and this defines the torus action.