An update for Fanography.info: description as zero sections of homogeneous vector bundles
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.