I'm interseted in blow-ups of toric varieties, unfortunately, I don't understand the construction of a blow-up built by a refinement of a fan, if to be more specific, I didn't find any constructions.
For example, let us consider a fan generated by rays (1,0,0), (0,1,0), (0,0,1), (-1,-1,-1), (1,1,1), (-1,0,0). First four rays give us $ \mathbb{C}P ^ 3$. How will our manifold change after adding rays (1,1,1), (-1,0,0) to a fan.
Where can I find something about connection of refinement of a fan with a blow-up of toric variety?