Mesut ŞAHİN
Summary: Toric Varieties and Toric Codes. The main theme of this part was the linear codes defined on zero-dimensional subvarieties of a toric variety over a finite field. We briefly discussed local structure of an abstract toric variety, namely we reviewed basics of (normal) affine toric varieties, (saturated) affine semigroups, toric ideals and their relations to strongly convex rational polyhedral cones. We discussed certain properties of projective toric varieties and gave several examples. We exhibited the precise relation between the combinatorics of a fan and the geometry of the corresponding normal toric variety. We also discussed the GIT quotient representation of a simplicial normal toric variety and introduced homogeneous coordinates as done for a projective space. These enabled us to introduce and study the main parameters of a toric code, i.e. an evaluation code defined on some subset of rational points on a normal toric variety over a finite field.