Livia Campo, Fano 3-folds and Equivariant Unprojections

The classification of terminal Fano 3-folds has been tackled from different directions: for instance, using the Minimal Model Program, via explicit Birational Geometry, and via Graded Rings methods. In this talk I would like to introduce the Graded Ring Database – an upper bound to the numerics of Fano 3-folds – and discuss the role it plays in the classification and construction of codimension 4 Fano 3-folds having Fano index 2.