Mathematics

The study of embeddings of algebraic tori into irreducible varieties has strong relation to the study of the geometry of convex bodies. We will consider varieties that are constructed from strongly convex cones and fans. In this seminar I will describe types of singularities of toric varieties and the resolutions of the singularities of toric surfaces. We will see Hirzebruch-Jung continued fractions playing to give the resolution of toric surfaces.  I will also try to give the idea how to generalize it in higher dimension.