In this talk, we will present the construction of toric varieties from fans and polytopes. We will give some properties of these varieties and study their various groups of divisors.
Then, following Klyachko, we will present the combinatorial description of equivariant reflexive sheaves in terms of families of filtrations.
The talk will be based on simple examples like projective space, Hirzebruch surfaces, tangent bundle, line bundles, etc...
