Fano 4-folds with large Picard number are products of surfaces
Let X be a smooth, complex Fano 4-fold, and ρ(X) its Picard number. We will discuss the following theorem: if ρ(X)>12, then X is a product of del Pezzo surfaces. This implies, in particular, that the maximal Picard number of a Fano 4-fold is 18. After an introduction and a discussion of examples, we explain some of the ideas and techniques involved in the proof.
