The topic of the course ¡­

The topic of the course will be the study of polarized varieties (X,L), where L is a very ample line bundle. We shall study properties of (X,L) related to jet bundles, dual varieties, osculating spaces, adjoint maps, nef value, etc. When X is a toric variety, (X,L) corresponds to a convex lattice polytope P. Our examples will mainly be toric, with a view towards showing how algebraic geometry can be translated into combinatorics of the polytope, and vice versa.

I will start by defining the jet bundles, a.k.a. Grothendieck's sheaves of principal parts and give a tour of their basic features: functoriality, geometric interpretation, local presentation, exact sequences, etc.