Deformations of smooth complete toric varieties

In the previous talk, I discussed deformation functors for smooth complete varieties. In this talk, I will turn to the case where X is a smooth complete toric variety, and the talk will be self-contained. Despite a theoretical understanding of the deformation functor Def_X, explicit computations are often challenging. For toric varieties, however, the combinatorial structure of the fan makes these computations far more tractable. I will describe the resulting combinatorial picture of Def_X and explain how it leads to explicit calculations. This is joint work with Nathan Ilten.