|Location:||MSRI: Baker Board Room|
Discrete problems have a natural translation into Algebraic Geometry( and vice-versa) thanks to the dictionary provided by toric
geometry. I will illustrate two problems where the algebro-geometrical solution provides information on the shape of the associated lattice polytope. The dual defect and an estimate on the nef value of a toric embedding forces the toric variety to be a fibration and the associated polytope to be a Cayley polytope. In the first part, the setting and the main results will be presented. During the second part the main ingredients in the proof will be illustrated and some open questions will be discussed. This is partly joint work with A. Dickenstein and R. Piene.