Descrizione
Abstract:
We study the class of smooth complex Fano varieties with Lefschetz defect 2 that arise from the blowing-up of a P^1-bundle over another Fano variety of lower dimension. More precisely, the blowing-up is performed along a codimension 2 smooth subvariety lying on a section of the P^1-bundle.
Although this construction may seem artificial, we observe that most of the known families of Fano 3-folds with Lefschetz defect 2 can be described by it. This might provide a more general and direct description than the well known case-by-case list by Mori and Mukai and might be helpful for the study of families of higher dimensional Fano varieties.