Speaker
Cinzia Casagrande
(Università di Torino)
Description
We will present some classification results for (smooth, complex) Fano 4-folds X with Picard number rho(X)>6. First of all, if rho(X)>9, then X is a product of del Pezzo surfaces; this is sharp, since we know one family of Fano 4-folds with rho(X)=9 that is not a product of surfaces. In the range rho(X)=7,8,9, we will explain some partial classification results, based on a detailed and explicit study of the geometry of X using birational geometry in the framework of the MMP. In particular, if rho(X)>6 and X has no small contractions, then either X is a product of surfaces, or rho(X)=7,8,9 and X is a blow-up of a cubic 4-fold along rho(X)-1 planes that intersect pairwise at a point.
Primary author
Cinzia Casagrande
(Università di Torino)
