Automorphisms of Fano threefolds

Abstract:

I will survey the results on automorphisms of Fano threefolds. In particular, I will speak about finiteness of automorphism groups (valid with a couple of explicitly described exceptions) and about the structure of Hilbert schemes of lines and conics that allows one to control the latter groups. Finally, I will describe some consequences for groups of birational automorphisms of rationally connected threefolds.