This will likely be the last post for 2020. Thank you all for reading, and see you in 2021!
If you are impatient: check out the big table.
In Fano 3-folds from homogeneous vector bundles over Grassmannians De Biase–Fatighenti–Tanturri obtained a description of a general member of each deformation family of Fano 3-folds as the zero locus of a homogeneous vector bundle in a product of Grassmannians and weighted projective spaces. Such description gives new tools to compute cohomological invariants of Fano 3-folds (by virtue of the Borel–Weil–Bott theorem), and gives a representation-theoretic flavour to the classification.
I wanted to add this information to Fanography, and I have finally done so now. Your patience will be rewarded by visiting the big table.
There could be some follow-up discussion on this description, but for now this is the end of the service announcement.