Abstract:
Groups of birational selfmaps of algebraic varieties may be large and
difficult to understand. On the other hand, the structure of their finite
subgroups is often much more accessible. One example is given by
K3 surfaces, whose automorphism group may be infinite but always
contains just a finite number of finite subgroups up to isomorphism.
I will survey the results on boundedness of finite groups acting by
automorphisms and birational automorphisms of algebraic varieties,
and discuss other examples with similar properties.
