Description:

Toric varieties are geometric objects defined combinatorially, much like CW complexes in topology. They can be used to study geometrically combinatorial objects like semigroups, cones, polytopes or simplicial complexes. In Algebraic Geometry, toric varieties are a rich source of explicit examples, a good testing ground for gaining intuition for open problems.

The first part of this course is a general introduction to toric varieties. We assume basic knowledge of Algebraic Geometry.
The second part tours several topics of birational geometry, in the special case of toric varieties. The goal is to construct many explicit examples: of singularities, polarized varieties, and varieties of K-pure type (Fano, Calabi-Yau, canonically polarized). We assume basic knowledge of Birational Geometry.
We also present the combinatorial counterpart of part two, essentially criteria to construct central lattice points in convex sets.

Personal Website：http://imar.ro/~fambro/ 

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